A354191 - OEIS

%I #8 May 20 2022 09:02:31

%S 0,3,-2,10,2,4,-8,4,-14,18,-8,16,6,4,8,32,10,4,-24,44,-32,24,-20,0,34,

%T 42,-92,24,-10,72,-24,224,-32,90,8,32,6,-12,24,32,18,16,-20,64,-16,44,

%U -28,48,-44,154,40,144,58,-68,48,-16,-96,22,-56,176,-6,24,-216,116,84,96,-68,220,-80,136,-16,-32,-36,90

%N a(n) = phi(A267099(sigma(n))) - phi(A267099(n)), where A267099 is fully multiplicative involution swapping the positions of 4k+1 and 4k+3 primes.

%H Antti Karttunen, <a href="/A354191/b354191.txt">Table of n, a(n) for n = 1..19683</a>

%F a(n) = A354190(n) - A354102(n).

%o (PARI) A354191(n) = (eulerphi(A267099(sigma(n))) - eulerphi(A267099(n))); \\ Uses the program given in A267099.

%Y Cf. A000010, A000203, A267099, A354102, A354106 (positions of 0's), A354190.

%Y Cf. also A353636.

%K sign

%O 1,2

%A _Antti Karttunen_, May 19 2022