# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a340368 Showing 1-1 of 1 %I A340368 #14 Nov 12 2022 05:34:46 %S A340368 1,1,2,3,4,2,6,9,8,4,10,6,12,6,8,27,16,8,18,12,12,10,22,18,24,12,32, %T A340368 18,28,8,30,81,20,16,24,24,36,18,24,36,40,12,42,30,32,22,46,54,48,24, %U A340368 32,36,52,32,40,54,36,28,58,24,60,30,48,243,48,20,66,48,44,24,70,72,72,36,48,54,60,24,78,108,128,40 %N A340368 Multiplicative with a(p^e) = (p - 1) * (p + 1)^(e-1). %H A340368 Antti Karttunen, Table of n, a(n) for n = 1..16383 %F A340368 a(n) = A167344(n) / A340323(n). %F A340368 a(n) = A173557(n) * A327564(n). %F A340368 Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 - 3/p^2 + 2/p^4) / Product_{p prime} (1 - 2/p^2 - 1/p^3) = 0.4313799748... . - _Amiram Eldar_, Nov 12 2022 %t A340368 f[p_, e_] := (p - 1)*(p + 1)^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 12 2022 *) %o A340368 (PARI) A340368(n) = if(1==n,n,my(f=factor(n)); prod(i=1,#f~,(f[i,1]-1)*((f[i,1]+1)^(f[i,2]-1)))); %Y A340368 Cf. A167344, A173557, A327564, A340323. %K A340368 nonn,mult %O A340368 1,3 %A A340368 _Antti Karttunen_, Jan 06 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE