A350073 a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.

1, 2, 1, 5, 2, 2, 1, 6, 11, 4, 2, 5, 5, 2, 2, 29, 4, 22, 3, 10, 1, 4, 2, 6, 29, 10, 3, 5, 6, 4, 1, 20, 2, 8, 2, 55, 17, 6, 5, 12, 10, 2, 7, 10, 22, 4, 2, 29, 34, 58, 4, 25, 8, 6, 4, 6, 3, 12, 6, 10, 29, 2, 11, 113, 10, 4, 13, 20, 2, 4, 4, 66, 31, 34, 29, 15, 2, 10, 3, 58, 49, 20, 10, 5, 8, 14, 6, 12, 12, 44, 5, 10

Offset: 1

Author

Antti Karttunen, Dec 12 2021

Keywords

• nonn
• mult

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)

Crossrefs

Cf. A000203, A064989, A161942, A337343 (a(n) >= n), A348748, A348749.

Cf. also A326042, A350072.

Programs

Mathematica

f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *)

PARI

A064989(n) = { my(f = factor(n)); for (i=1, #f~, f[i,1] = if(2==f[i, 1],1,precprime(f[i, 1]-1))); factorback(f); };
A350073(n) = A064989(sigma(n));

Formula

Multiplicative with a(p^e) = A064989(1 + p + p^2 + ... + p^e).

a(n) = A064989(A000203(n)) = A064989(A161942(n)).