cp's OEIS Frontend

A347231 Difference between A344695 [gcd(psi(n),sigma(n))] and its Möbius transform.

%I A347231 #10 Aug 30 2021 21:52:55
%S A347231 0,1,1,3,1,6,1,1,4,8,1,10,1,10,9,3,1,9,1,16,11,14,1,6,6,16,1,22,1,42,
%T A347231 1,1,15,20,13,-5,1,22,17,8,1,54,1,34,21,26,1,10,8,13,21,40,1,6,17,10,
%U A347231 23,32,1,54,1,34,29,3,19,78,1,52,27,74,1,9,1,40,19,58,19,90,1,16,4,44,1,74,23,46,33,14,1,48
%N A347231 Difference between A344695 [gcd(psi(n),sigma(n))] and its Möbius transform.
%H A347231 Antti Karttunen, <a href="/A347231/b347231.txt">Table of n, a(n) for n = 1..16384</a>
%F A347231 a(n) = A344695(n) - A347230(n).
%F A347231 a(n) = -Sum_{d|n, d<n} A008683(n/d) * A344695(d).
%o A347231 (PARI)
%o A347231 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A347231 A344695(n) = gcd(sigma(n), A001615(n));
%o A347231 A347231(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A344695(d));
%Y A347231 Cf. A000203, A001615, A008683, A344695, A347230.
%Y A347231 Cf. also A347229.
%K A347231 sign
%O A347231 1,4
%A A347231 _Antti Karttunen_, Aug 25 2021