A348049 a(n) = A003959(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, 9, 1, 1, 1, 9, 16, 1, 1, 9, 1, 1, 1, 81, 1, 16, 1, 9, 1, 1, 1, 9, 36, 1, 8, 9, 1, 1, 1, 27, 1, 1, 1, 144, 1, 1, 1, 9, 1, 1, 1, 9, 16, 1, 1, 81, 64, 36, 1, 9, 1, 8, 1, 9, 1, 1, 1, 9, 1, 1, 16, 729, 1, 1, 1, 9, 1, 1, 1, 144, 1, 1, 36, 9, 1, 1, 1, 81, 256, 1, 1, 9, 1, 1, 1, 9, 1, 16, 1, 9, 1, 1, 1, 27, 1, 64

Offset

1,4

Comments

Not multiplicative. For example, a(196) = 192 != 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) = A003959(n) / A348047(n) = A003959(n) / gcd(A000203(n), A003959(n)).

Mathematica

f[p_, e_] := (p + 1)^e; a[1] = 1; a[n_] := (m = Times @@ f @@@ FactorInteger[n]) / GCD[m, DivisorSigma[1, 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); };
A348049(n) = { my(u=A003959(n)); (u/gcd(u, sigma(n))); };

Crossrefs

Cf. A000203, A003959, A005117 (positions of 1's), A348029, A348047, A348048.

Cf. also A344697.

Sequence in context: A010164 A006084 A059928 * A293724 A283989 A361794

Adjacent sequences: A348046 A348047 A348048 * A348050 A348051 A348052

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved