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A349726
Numbers k >= 1 such that A018804(k) divided by A000203(k) is an integer.
0
1, 2, 40, 44, 220, 252, 752, 980, 2940, 3680, 4508, 10080, 10780, 11016, 12224, 14432, 16072, 17384, 26096, 26216, 36672, 36848, 44064, 45792, 55080, 60588, 61120, 64288, 72160, 80360, 82656, 85536, 88396, 88944, 93568, 95256, 112000, 112572, 120320, 134464, 144752
OFFSET
1,2
EXAMPLE
k = 40 : A018804(40) = 180, A000203(40) = 90, 180/90 = 2 thus 40 is a term.
MATHEMATICA
A018804[n_]:=Apply[Times, Apply[((#1-1)#2/#1+1)#1^#2&, FactorInteger[n], {1}]]; (* After Amiram Eldar in A018804 *)
upto=10^5; Reap[Do[If[IntegerQ[A018804[k]/DivisorSigma[1, k]], Sow[k]], {k, upto}]][[-1, -1]] (* Paolo Xausa, Aug 18 2022 *)
PROG
(PARI) isok(k) = (sumdiv(k, d, k*eulerphi(d)/d) % sigma(k)) == 0; \\ Michel Marcus, Nov 27 2021
CROSSREFS
Sequence in context: A047660 A213909 A349717 * A275547 A269544 A281761
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Nov 27 2021
EXTENSIONS
a(12)-a(36) from Paolo Xausa, Nov 27 2021
More terms from Amiram Eldar, Nov 27 2021
STATUS
approved