A337338 Numerator of (1+sigma(s)) / ((s+1)/2), where s is the square of n prime-shifted once (s = A003961(n)^2 = A003961(n^2)).

2, 14, 32, 122, 58, 404, 134, 1094, 782, 742, 184, 3752, 308, 346, 1768, 9842, 382, 10154, 554, 6898, 4124, 2380, 872, 33884, 2802, 3992, 19532, 1238, 994, 22972, 1408, 88574, 5674, 4954, 7582, 94502, 1724, 7190, 9518, 62302, 1894, 53600, 2258, 22144, 44518, 11324, 2864, 305072, 16106, 36414, 11812, 37148, 3542, 253904

Offset: 1

Author

Antti Karttunen, Aug 24 2020

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A003961, A003973, A048673, A336697, A336844, A337194, A337337.

Cf. A337339 (denominators).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337338(n) = { my(s=(A003961(n)^2),t=1+sigma(s)); (t/gcd(t, (s+1)/2)); };
\\ Or as:
A337338(n) = { my(s=A003961(n^2)); numerator((1+sigma(s))/((s+1)/2)); };

Formula

a(n) = A337194(A003961(n)^2) / A337337(n).