A351456 a(n) = A003958(sigma(A003961(n))), where A003958 is multiplicative with a(p^e) = (p-1)^e, A003961 multiplicative with a(prime(k)^e) = prime(1+k)^e, and sigma is the sum of divisors function.

1, 1, 2, 12, 1, 2, 2, 4, 30, 1, 6, 24, 4, 2, 2, 100, 4, 30, 2, 12, 4, 6, 8, 8, 36, 4, 24, 24, 1, 2, 18, 72, 12, 4, 2, 360, 12, 2, 8, 4, 10, 4, 2, 72, 30, 8, 8, 200, 108, 36, 8, 48, 8, 24, 6, 8, 4, 1, 30, 24, 16, 18, 60, 1092, 4, 12, 4, 48, 16, 2, 36, 120, 4, 12, 72, 24, 12, 8, 12, 100, 700, 10, 16, 48, 4, 2, 2, 24

Offset

1,3

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

Multiplicative with a(p^e) = A003958(1 + q + ... + q^e), where q = nextPrime(p) = A151800(p).

a(n) = A003958(A003973(n)) = A351442(A003961(n)) = A003958(A000203(A003961(n))).

a(n) = A351457(n) + A339905(n).

Prog

(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351456(n) = A003958(sigma(A003961(n)));

Crossrefs

Cf. A000203, A003958, A003961, A003973, A151800, A339905, A351442, A351457.

Cf. also A326042.

Sequence in context: A160367 A016736 A287704 * A082185 A354130 A113491

Adjacent sequences: A351453 A351454 A351455 * A351457 A351458 A351459

Keyword

nonn,mult

Author

Antti Karttunen, Feb 12 2022

Status

approved