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A325277
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Irregular triangle read by rows where row 1 is {1} and row n is the sequence starting with n and repeatedly applying A181819 until a prime number is reached.
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48
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1, 2, 3, 4, 3, 5, 6, 4, 3, 7, 8, 5, 9, 3, 10, 4, 3, 11, 12, 6, 4, 3, 13, 14, 4, 3, 15, 4, 3, 16, 7, 17, 18, 6, 4, 3, 19, 20, 6, 4, 3, 21, 4, 3, 22, 4, 3, 23, 24, 10, 4, 3, 25, 3, 26, 4, 3, 27, 5, 28, 6, 4, 3, 29, 30, 8, 5, 31, 32, 11, 33, 4, 3
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OFFSET
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1,2
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COMMENTS
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The function A181819 maps p^i*...*q^j to prime(i)*...*prime(j) where p through q are distinct primes.
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LINKS
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Table of n, a(n) for n=1..73.
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FORMULA
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T(n,k) = A325239(n,k) for k <= A323014(n).
A001222(T(n,k)) = A323023(n,k) for n > 1.
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EXAMPLE
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Triangle begins:
1 26 4 3 51 4 3 76 6 4 3
2 27 5 52 6 4 3 77 4 3
3 28 6 4 3 53 78 8 5
4 3 29 54 10 4 3 79
5 30 8 5 55 4 3 80 14 4 3
6 4 3 31 56 10 4 3 81 7
7 32 11 57 4 3 82 4 3
8 5 33 4 3 58 4 3 83
9 3 34 4 3 59 84 12 6 4 3
10 4 3 35 4 3 60 12 6 4 3 85 4 3
11 36 9 3 61 86 4 3
12 6 4 3 37 62 4 3 87 4 3
13 38 4 3 63 6 4 3 88 10 4 3
14 4 3 39 4 3 64 13 89
15 4 3 40 10 4 3 65 4 3 90 12 6 4 3
16 7 41 66 8 5 91 4 3
17 42 8 5 67 92 6 4 3
18 6 4 3 43 68 6 4 3 93 4 3
19 44 6 4 3 69 4 3 94 4 3
20 6 4 3 45 6 4 3 70 8 5 95 4 3
21 4 3 46 4 3 71 96 22 4 3
22 4 3 47 72 15 4 3 97
23 48 14 4 3 73 98 6 4 3
24 10 4 3 49 3 74 4 3 99 6 4 3
25 3 50 6 4 3 75 6 4 3 100 9 3
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MATHEMATICA
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red[n_]:=Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]];
Table[NestWhileList[red, n, #>1&&!PrimeQ[#]&], {n, 30}]
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CROSSREFS
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Row lengths are 1 for n = 1 and A323014(n) for n > 1.
Cf. A001221, A001222, A071625, A118914, A181819, A181821, A182850, A182857, A323022, A323023, A325238, A325239.
Sequence in context: A305747 A304736 A286448 * A257573 A182973 A360565
Adjacent sequences: A325274 A325275 A325276 * A325278 A325279 A325280
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KEYWORD
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nonn,tabf
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AUTHOR
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Gus Wiseman, Apr 15 2019
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STATUS
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approved
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