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A324851
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Numbers > 1 divisible by the sum of their prime indices.
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19
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2, 4, 6, 12, 15, 16, 20, 30, 35, 36, 42, 48, 56, 88, 99, 112, 120, 126, 130, 135, 143, 144, 160, 162, 180, 192, 210, 216, 220, 221, 228, 231, 242, 250, 256, 270, 275, 280, 288, 297, 300, 308, 322, 330, 338, 360, 396, 400, 408, 429, 435, 440, 455, 468, 480, 493
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The sum of prime indices of n is A056239(n). For example, the prime indices of 99 are {2,2,5}, with sum 9, a divisor of 99, so 99 is in the sequence.
For any k>=2, let d be a divisor of k such that d > A056239(k). Then 2^(d-A056239(k))*k is in the sequence. Similarly if k is in the sequence with d = A056239(k), then 2^d*k is in the sequence. - Robert Israel, Mar 19 2019
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
6: {1,2}
12: {1,1,2}
15: {2,3}
16: {1,1,1,1}
20: {1,1,3}
30: {1,2,3}
35: {3,4}
36: {1,1,2,2}
42: {1,2,4}
48: {1,1,1,1,2}
56: {1,1,1,4}
88: {1,1,1,5}
99: {2,2,5}
112: {1,1,1,1,4}
120: {1,1,1,2,3}
126: {1,2,2,4}
130: {1,3,6}
135: {2,2,2,3}
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MAPLE
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filter:= proc(n) local t; n mod add(numtheory:-pi(t[1])*t[2], t=ifactors(n)[2]) = 0 end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 19 2019
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MATHEMATICA
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Select[Range[2, 100], Divisible[#, Plus@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]*k]]&]
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PROG
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(PARI) isok(n) = {my(f = factor(n)); (n!=1) && !(n % sum(k=1, #f~, primepi(f[k, 1])*f[k, 2])); } \\ Michel Marcus, Mar 19 2019
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CROSSREFS
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Cf. A003963, A036844, A056239, A112798, A120383, A290822, A306844.
Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324847, A324848, A324849, A324850, A324852.
Sequence in context: A057830 A013916 A141113 * A348572 A334156 A255001
Adjacent sequences: A324848 A324849 A324850 * A324852 A324853 A324854
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 18 2019
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STATUS
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approved
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