A351425 If n = p_1^e_1 * ... * p_k^e_k, where p_1 < ... < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k + 1)^(e_k - 1); a(1) = 1.

1, 1, 1, 3, 1, 2, 1, 9, 4, 2, 1, 4, 1, 2, 3, 27, 1, 8, 1, 4, 3, 2, 1, 8, 6, 2, 16, 4, 1, 6, 1, 81, 3, 2, 5, 16, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 8, 12, 3, 4, 1, 32, 5, 8, 3, 2, 1, 12, 1, 2, 9, 243, 5, 6, 1, 4, 3, 10, 1, 32, 1, 2, 18, 4, 7, 6, 1, 16, 64, 2

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

a[n_] := Module[{f = FactorInteger[n]}, n*(f[[-1, 1]] + 1)^(f[[-1, 2]] - 1)/f[[-1, 1]]^f[[-1, 2]]]; a[1] = 1; Array[a, 100]

Crossrefs

Cf. A351168, A351419.

Sequence in context: A226629 A349620 A349380 * A249580 A340147 A011086

Adjacent sequences: A351422 A351423 A351424 * A351426 A351427 A351428

Keyword

nonn

Author

Amiram Eldar and N. J. A. Sloane, Feb 11 2022

Status

approved