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A354563
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Numbers k such that P(k)^2 | k and P(k+1)^3 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
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5
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242, 2400, 6859, 10647, 47915, 57121, 344604, 499999, 830465, 1012499, 1431125, 2098853, 2825760, 2829123, 3930399, 5560691, 11859210, 12323584, 13137830, 18253460, 18279039, 21093749, 30664296, 32279841, 33999932, 37218852, 38640401, 38740085, 41485688, 45222737
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Daniel Suteu, Table of n, a(n) for n = 1..9503 (terms <= 10^15)
Jean-Marie De Koninck and Matthieu Moineau, Consecutive Integers Divisible by a Power of their Largest Prime Factor, J. Integer Seq., Vol. 21 (2018), Article 18.9.3.
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EXAMPLE
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242 = 2 * 11^2 is a term since P(242) = 11 and 11^2 | 242, 243 = 3^5, P(243) = 3, and 3^3 | 243.
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MATHEMATICA
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p[n_] := FactorInteger[n][[-1, 2]]; Select[Range[10^6], p[#] > 1 && p[# + 1] > 2 &]
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PROG
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(Python)
from sympy import factorint
def c(n, e): f = factorint(n); return f[max(f)] >= e
def ok(n): return n > 1 and c(n, 2) and c(n+1, 3)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 30 2022
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CROSSREFS
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Subsequence of A070003 and A354558.
A354562 is a subsequence.
Cf. A006530, A071178, A354564.
Sequence in context: A234484 A160551 A258886 * A354565 A165935 A318529
Adjacent sequences: A354560 A354561 A354562 * A354564 A354565 A354566
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, May 30 2022
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STATUS
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approved
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