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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.
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%I #25 Feb 11 2022 05:29:22

%S 1,1,4,1,16,8,36,1,8,32,100,16,144,72,48,1,256,16,324,64,108,200,484,

%T 32,64,288,16,144,784,96,900,1,300,512,180,32,1296,648,432,128,1600,

%U 216,1764,400,144,968,2116,64,216,128,768,576,2704,32,500,288,972,1568

%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="/A351419/b351419.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] (* _Amiram Eldar_, Feb 11 2022 *)

%Y Inspired by A351168.

%Y Cf. A351425.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Feb 11 2022