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A336457 a(n) = A065330(sigma(n)), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

%I A336457 #12 Jul 25 2020 10:36:26
%S A336457 1,1,1,7,1,1,1,5,13,1,1,7,7,1,1,31,1,13,5,7,1,1,1,5,31,7,5,7,5,1,1,7,
%T A336457 1,1,1,91,19,5,7,5,7,1,11,7,13,1,1,31,19,31,1,49,1,5,1,5,5,5,5,7,31,1,
%U A336457 13,127,7,1,17,7,1,1,1,65,37,19,31,35,1,7,5,31,121,7,7,7,1,11,5,5,5,13,7,7,1,1,5,7,49
%N A336457 a(n) = A065330(sigma(n)), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.
%C A336457 Sequence removes prime factors 2 and 3 from the prime factorization of the sum of divisors of n.
%H A336457 Antti Karttunen, <a href="/A336457/b336457.txt">Table of n, a(n) for n = 1..10000</a>
%H A336457 Antti Karttunen, <a href="/A336457/a336457.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336457 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336457 a(n) = A065330(A000203(n)) = A038502(A161942(n)).
%F A336457 Multiplicative with a(p^e) = A065330(1 + p + p^2 + ... + p^e).
%t A336457 Array[Times @@ Map[#1^#2 & @@ # &, DeleteCases[FactorInteger[DivisorSigma[1, #]], _?(First@ # <= 3 &)]] &, 97] (* _Michael De Vlieger_, Jul 24 2020 *)
%o A336457 (PARI)
%o A336457 A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
%o A336457 A336457(n) = A065330(sigma(n));
%Y A336457 Cf. A000203, A038502, A065330, A161942, A336458.
%Y A336457 Cf. also A336455.
%K A336457 nonn,mult
%O A336457 1,4
%A A336457 _Antti Karttunen_, Jul 24 2020