A337338 - OEIS

%I #6 Aug 24 2020 22:29:44

%S 2,14,32,122,58,404,134,1094,782,742,184,3752,308,346,1768,9842,382,

%T 10154,554,6898,4124,2380,872,33884,2802,3992,19532,1238,994,22972,

%U 1408,88574,5674,4954,7582,94502,1724,7190,9518,62302,1894,53600,2258,22144,44518,11324,2864,305072,16106,36414,11812,37148,3542,253904

%N 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)).

%H Antti Karttunen, <a href="/A337338/b337338.txt">Table of n, a(n) for n = 1..10000</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 a(n) = A337194(A003961(n)^2) / A337337(n).

%o (PARI)

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

%o A337338(n) = { my(s=(A003961(n)^2),t=1+sigma(s)); (t/gcd(t, (s+1)/2)); };

%o \\ Or as:

%o A337338(n) = { my(s=A003961(n^2)); numerator((1+sigma(s))/((s+1)/2)); };

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

%Y Cf. A337339 (denominators).

%K nonn,frac

%O 1,1

%A _Antti Karttunen_, Aug 24 2020