cp's OEIS Frontend

A353790 a(n) = A353749(sigma(A003961(n))), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes, while A003961 shifts the factorization one step towards higher primes.

%I A353790 #14 May 13 2022 14:06:35
%S A353790 1,2,4,132,4,16,8,48,870,16,30,528,24,32,32,5390,24,1740,16,528,96,
%T A353790 120,48,384,1224,96,1056,1056,16,128,306,7920,240,96,64,114840,120,64,
%U A353790 288,384,140,384,32,3960,3480,192,144,21560,9180,2448,192,3168,96,4224,240,768,192,64,870,4224,416,1224,6960,1191372,192
%N A353790 a(n) = A353749(sigma(A003961(n))), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes, while A003961 shifts the factorization one step towards higher primes.
%C A353790 See comments in A353789.
%H A353790 Antti Karttunen, <a href="/A353790/b353790.txt">Table of n, a(n) for n = 1..10000</a>
%H A353790 Antti Karttunen, <a href="/A353790/a353790.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A353790 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353790 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A353790 a(n) = A353750(A003961(n)) = A326042(n) * A353767(n).
%F A353790 a(n) = A000010(A003973(n)) * A064989(A003973(n)).
%o A353790 (PARI)
%o A353790 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A353790 A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
%o A353790 A353790(n) = { my(s=sigma(A003961(n))); (eulerphi(s)*A064989(s)); };
%Y A353790 Cf. A003961, A003973, A064989, A326042, A353750, A353767, A353789.
%Y A353790 Cf. also A353794.
%K A353790 nonn
%O A353790 1,2
%A A353790 _Antti Karttunen_, May 10 2022