login
a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).
7

%I #15 May 13 2022 14:07:26

%S 1,1,4,132,1,4,4,12,870,1,30,528,16,4,4,4900,12,870,4,132,16,30,48,48,

%T 1224,16,528,528,1,4,306,3960,120,12,4,114840,120,4,64,12,70,16,4,

%U 3960,870,48,64,19600,9180,1224,48,2112,48,528,30,48,16,1,870,528,208,306,3480,1191372,16,120,16,1584,192,4,1116

%N a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).

%C It is conjectured that a(n) is not a multiple of A353793(n) on any other n except on n=1. See also A353795.

%H Antti Karttunen, <a href="/A353794/b353794.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A353794/a353794.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F Multiplicative with a(p^e) = A003958(1 + q + ... + q^e) * A064989(1 + q + ... + q^e), where q is the least prime larger than p.

%F a(n) = A353791(A003973(n)) = A353792(A003961(n)).

%F a(n) = A326042(n) * A351456(n) = A064989(A003973(n)) * A003958(A003973(n)).

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A353794(n) = { my(s=sigma(A003961(n))); (A003958(s)*A064989(s)); };

%Y Cf. A000203, A003958, A003961, A003973, A064989, A326042, A351456, A353791, A353792, A353793, A353795 [numbers k such that k divides a(k)].

%Y Cf. also A353790.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, May 11 2022