A348499 Numbers k such that A003968(k) is a multiple of k, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119

Offset: 1

Author

Antti Karttunen, Oct 29 2021

Keywords

• nonn

Comments

This is a subsequence of A333634. See comments in A347892.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Union of A005117 and A347892 (terms that are not squarefree).

Subsequence of A333634.

Positions of ones in A348037.

Cf. A003968, A348030, A348036, A347960.

Programs

Mathematica

f[p_, e_] := p*(p + 1)^(e - 1); s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[120], Divisible[s[#], #] &] (* Amiram Eldar, Oct 29 2021 *)

PARI

A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
isA348499(n) = !(A003968(n)%n);