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%I #12 Jul 23 2022 09:56:07
%S 1,1,2,1,2,12,4,5,1,2,2,2,2,24,24,1,2,1,4,2,8,4,6,60,1,6,4,4,2,24,2,7,
%T 12,2,48,13,2,12,4,10,2,96,4,14,2,24,6,2,19,3,24,2,6,24,8,120,16,2,2,
%U 24,2,8,4,1,12,48,4,2,12,48,2,5,2,6,2,4,24,24,4,2,11,2,6,8,4,12,24,20,2,2,8,6,4,72,24
%N a(n) = gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).
%H Antti Karttunen, <a href="/A355932/b355932.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A355932/a355932.txt">Data supplement: n, a(n) computed for n = 1..100000</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) = gcd(A000203(n), A003973(n)).
%F a(n) = A003973(n) / A355933(n).
%F a(n) = A000203(n) / A355934(n).
%t f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := GCD[DivisorSigma[1, n], Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Jul 22 2022 *)
%o (PARI)
%o A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
%o A355932(n) = gcd(sigma(n), A003973(n));
%Y Cf. A000203, A003961, A003973, A355933, A355934.
%Y Cf. also A336850, A342671.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jul 22 2022