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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).

%I A348499 #18 Feb 10 2022 20:06:36
%S A348499 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,
%T A348499 38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,72,73,
%U A348499 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
%N 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).
%C A348499 This is a subsequence of A333634. See comments in A347892.
%H A348499 Antti Karttunen, <a href="/A348499/b348499.txt">Table of n, a(n) for n = 1..20000</a>
%t A348499 f[p_, e_] := p*(p + 1)^(e - 1); s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[120], Divisible[s[#], #] &] (* _Amiram Eldar_, Oct 29 2021 *)
%o A348499 (PARI)
%o A348499 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); }
%o A348499 isA348499(n) = !(A003968(n)%n);
%Y A348499 Union of A005117 and A347892 (terms that are not squarefree).
%Y A348499 Subsequence of A333634.
%Y A348499 Positions of ones in A348037.
%Y A348499 Cf. A003968, A348030, A348036, A347960.
%K A348499 nonn
%O A348499 1,2
%A A348499 _Antti Karttunen_, Oct 29 2021