A348048 a(n) = sigma(n) / gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.

1, 1, 1, 7, 1, 1, 1, 5, 13, 1, 1, 7, 1, 1, 1, 31, 1, 13, 1, 7, 1, 1, 1, 5, 31, 1, 5, 7, 1, 1, 1, 7, 1, 1, 1, 91, 1, 1, 1, 5, 1, 1, 1, 7, 13, 1, 1, 31, 57, 31, 1, 7, 1, 5, 1, 5, 1, 1, 1, 7, 1, 1, 13, 127, 1, 1, 1, 7, 1, 1, 1, 65, 1, 1, 31, 7, 1, 1, 1, 31, 121, 1, 1, 7, 1, 1, 1, 5, 1, 13, 1, 7, 1, 1, 1, 7, 1, 57, 13

Offset

1,4

Comments

Not multiplicative. For example, a(196) = 133 != a(4) * a(49).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

a(n) = A000203(n) / A348047(n) = A000203(n) / gcd(A000203(n), A003959(n)).

Mathematica

f[p_, e_] := (p + 1)^e; a[1] = 1; a[n_] := (s = DivisorSigma[1, n]) / GCD[s, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Oct 21 2021 *)

Prog

(PARI)
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348048(n) = { my(u=sigma(n)); (u/gcd(u, A003959(n))); };

Crossrefs

Cf. A000203, A003959, A348029, A348047, A348049.

Cf. also A344696.

Sequence in context: A072101 A366894 A088840 * A348985 A348504 A344696

Adjacent sequences: A348045 A348046 A348047 * A348049 A348050 A348051

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved