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A353792 a(n) = A003958(sigma(n)) * A064989(sigma(n)).

%I A353792 #12 May 13 2022 14:07:14
%S A353792 1,4,1,30,4,4,1,48,132,16,4,30,30,4,4,870,16,528,12,120,1,16,4,48,870,
%T A353792 120,12,30,48,16,1,480,4,64,4,3960,306,48,30,192,120,4,70,120,528,16,
%U A353792 4,870,1224,3480,16,900,64,48,16,48,12,192,48,120,870,4,132,14238,120,16,208,480,4,16,16,6336,1116,1224,870
%N A353792 a(n) = A003958(sigma(n)) * A064989(sigma(n)).
%H A353792 Antti Karttunen, <a href="/A353792/b353792.txt">Table of n, a(n) for n = 1..10000</a>
%H A353792 Antti Karttunen, <a href="/A353792/a353792.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A353792 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353792 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A353792 Multiplicative with a(p^e) = A003958(1 + p + ... + p^e) * A064989(1 + p + ... + p^e).
%F A353792 a(n) = A353791(A000203(n)).
%F A353792 a(n) = A351442(n) * A350073(n) = A003958(A000203(n)) * A064989(A000203(n)).
%o A353792 (PARI)
%o A353792 A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o A353792 A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353792 A353792(n) = { my(s=sigma(n)); (A003958(s)*A064989(s)); };
%o A353792 (PARI) A353792(n) = { my(f=factor(n),s); prod(i=1, #f~, s = sigma(f[i,1]^f[i,2]); A003958(s)*A064989(s)); };
%Y A353792 Cf. A003958, A064989, A350073, A351442, A353791, A353793, A353794 [= a(A003961(n))].
%Y A353792 Cf. A046528 (positions of 1's).
%Y A353792 Cf. also A353750.
%K A353792 nonn,mult
%O A353792 1,2
%A A353792 _Antti Karttunen_, May 11 2022