A324340 a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.

1, -3, -4, 2, -6, 12, 3, 0, -8, 18, 24, -8, 5, -9, 0, 0, -12, 24, 32, -12, 48, -72, -18, 0, 7, -15, -20, 6, 0, 0, 0, 0, -14, 36, 48, -16, 72, -96, -24, 0, 96, -144, -192, 48, -40, 54, 0, 0, 11, -21, -28, 10, -42, 60, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 42, 56, -24, 84, -144, -36, 0, 112, -216, -288, 64, -60, 72, 0, 0, 168, -288, -384, 96, -576, 576, 144, 0

Offset: 0

Author

Antti Karttunen, Feb 24 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005940, A046692.

Cf. also A323915, A324335, A324336, A324339.

Programs

PARI

A324340(n) = { my(m1=1, p=2); while(n, if(!(n%2), p=nextprime(1+p); n>>=1, if(1==(n%4), m1 *= -(1+p), if(3==(n%8), m1 *= p, return(0))); while((n%2),n>>=1))); (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
A046692(n) = { my(f=factor(n)~); prod(i=1, #f, if(1==f[2,i], -(f[1,i]+1), if(2==f[2,i], f[1,i], 0))); };
A324340(n) = A046692(A005940(1+n));

Formula

a(n) = A046692(A005940(1+n)).