A355932 a(n) = gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jul 22 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A355933, A355934.

Cf. also A336850, A342671.

Programs

Mathematica

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 *)

PARI

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A355932(n) = gcd(sigma(n), A003973(n));

Formula

a(n) = gcd(A000203(n), A003973(n)).

a(n) = A003973(n) / A355933(n).

a(n) = A000203(n) / A355934(n).