cp's OEIS Frontend

A342917 a(n) = A001615(n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

%I A342917 #10 Mar 30 2021 15:19:09
%S A342917 1,1,1,6,1,12,1,4,6,18,1,24,1,8,3,24,1,36,1,12,16,36,1,48,15,14,9,48,
%T A342917 1,72,1,16,24,54,4,72,1,20,7,72,1,96,1,8,36,72,1,96,28,30,18,84,1,108,
%U A342917 9,32,40,90,1,144,1,32,3,96,14,144,1,36,48,144,1,144,1,38,30,120,16,168,1,16,54,126,1,192,54,44,15,144
%N A342917 a(n) = A001615(n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
%C A342917 The scatter plot shows two distinct "fans" separated by a gap. Why?
%H A342917 Antti Karttunen, <a href="/A342917/b342917.txt">Table of n, a(n) for n = 1..16384</a>
%F A342917 a(n) = A001615(n) / A342915(n) = A001615(n) / gcd(1+n, A001615(n)).
%o A342917 (PARI)
%o A342917 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 A342917 A342917(n) = { my(u=A001615(n)); (u/gcd(1+n,u)); };
%Y A342917 Cf. A001615, A342915, A342916.
%Y A342917 Cf. also A160595.
%K A342917 nonn,look
%O A342917 1,4
%A A342917 _Antti Karttunen_, Mar 29 2021