A324052 a(n) = A083254(A005940(1+n)).

1, 0, 1, 0, 3, -2, 3, 0, 5, -2, 1, -4, 15, -6, 9, 0, 9, -2, 3, -4, 13, -14, 3, -8, 35, -10, 5, -12, 75, -18, 27, 0, 11, -2, 7, -4, 25, -18, 9, -8, 43, -22, -9, -28, 65, -42, 9, -16, 99, -14, 21, -20, 91, -70, 15, -24, 245, -50, 25, -36, 375, -54, 81, 0, 15, -2, 9, -4, 31, -26, 21, -8, 53, -30, -5, -36, 125, -54, 27, -16, 97, -34, 9

Offset: 0

Author

Antti Karttunen, Feb 18 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Crossrefs

Cf. A005940, A083254, A054429, A290077, A324055, A324182.

Cf. also A324103.

Programs

PARI

A324052(n) = { my(m1=1,m2=2,p=2); while(n, if(!(n%2), p=nextprime(1+p), m1 *= p; m2 *= (p-(1==(n%4)))); n>>=1); (m2-m1); };

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A083254(n) = (2*eulerphi(n)-n);
A324052(n) = A083254(A005940(1+n));

Formula

a(n) = A083254(A005940(1+n)).

a(n) = 2*A290077(n) - A005940(1+n).

For n >= 1, a(n) = A324182(A054429(n)).

For n >= 1, a((2^n)-1) = 0.