|
%I #15 Dec 15 2022 06:17:14
%S 1,1,4,1,16,4,36,1,16,16,100,4,144,36,64,1,256,16,324,16,144,100,484,
%T 4,256,144,64,36,784,64,900,1,400,256,576,16,1296,324,576,16,1600,144,
%U 1764,100,256,484,2116,4,1296,256
%N Totally multiplicative sequence with a(p) = (p-1)^2 = p^2-2p+1 for prime p.
%H G. C. Greubel, <a href="/A167343/b167343.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = ((p-1)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)^2)^e(k).
%F a(n) = A003958(n)^2.
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 1/p^3 - 1/p^4) = 0.1229567616... . - _Amiram Eldar_, Dec 15 2022
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]^2, {n, 1, 100}] (* _G. C. Greubel_, Jun 10 2016 *)
%Y Cf. A003958.
%K nonn,mult
%O 1,3
%A _Jaroslav Krizek_, Nov 01 2009
|
