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A353764 Numbers k for which A353749(sigma(k)) is a multiple of A353749(k), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.

%I A353764 #16 May 12 2022 16:12:46
%S A353764 1,2,4,6,8,10,18,20,24,28,30,32,40,60,72,84,90,108,120,128,200,216,
%T A353764 224,234,252,360,384,496,600,640,672,864,936,1080,1120,1152,1170,1488,
%U A353764 1800,1920,2016,2176,3200,3360,3456,4320,4464,4680,5148,5600,5760,6048,6528,6552,8128,9600,10080,10880,14976,16800,17280
%N A353764 Numbers k for which A353749(sigma(k)) is a multiple of A353749(k), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.
%C A353764 Question: Are there any odd terms after the initial one? See A353789, A353796, A353797.
%H A353764 Antti Karttunen, <a href="/A353764/b353764.txt">Table of n, a(n) for n = 1..229; terms <= 2^32</a>
%H A353764 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A353764 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353764 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A353764 f[p_, e_] := (p - 1)*p^(e - 1)*If[p == 2, 1, NextPrime[p, -1]^e]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[20000], Divisible[s[DivisorSigma[1, #]], s[#]] &] (* _Amiram Eldar_, May 10 2022 *)
%o A353764 (PARI)
%o A353764 A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353764 A353749(n) = (eulerphi(n)*A064989(n));
%o A353764 isA353764(n) = { my(s=sigma(n)); !(A353749(s)%A353749(n)); };
%Y A353764 Cf. A000010, A000203, A006872, A062401, A064989, A336549, A336550, A353757, A353761, A353766 (characteristic function), A353789, A353796, A353797.
%Y A353764 Positions of 1's in A353762. Cf. also A353765.
%Y A353764 Subsequence of A353759. Cf. A007691 (a subsequence).
%K A353764 nonn
%O A353764 1,2
%A A353764 _Antti Karttunen_, May 10 2022