A351425 - OEIS

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.

%I #15 Feb 11 2022 05:28:44

%S 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,

%T 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,

%U 5,6,1,4,3,10,1,32,1,2,18,4,7,6,1,16,64,2

%N 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.

%H Amiram Eldar, <a href="/A351425/b351425.txt">Table of n, a(n) for n = 1..10000</a>

%t 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]

%Y Cf. A351168, A351419.

%K nonn

%O 1,4

%A _Amiram Eldar_ and _N. J. A. Sloane_, Feb 11 2022