A369460 Number of representations of 12n-9 as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

0, 0, 1, 1, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 0, 1, 2, 0, 0, 3, 0, 2, 1, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 0, 1, 1, 1, 0, 2, 0, 2, 3, 0, 2, 3, 0, 1, 0, 2, 1, 1, 0, 2, 1, 0, 1, 1, 0, 3, 1, 2, 1, 0, 0, 3, 2, 1, 1, 2, 0, 1, 3, 2, 1, 1, 2, 1, 0, 2, 2, 3, 0, 1, 2, 0, 4, 1, 0, 2, 1, 0, 0, 2, 2

Offset: 1

Author

Antti Karttunen, Jan 23 2024

Keywords

• nonn

Comments

See A369450 for the cumulative sum, and comments there.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Trisection of A369055.

Cf. A369054, A369248 (gives the positions of 0's in this sequence when nine is added and divided by 12), A369450 (partial sums), A369461, A369462.

Programs

PARI

A369054(n) = if(3!=(n%4),0, my(v = [3,3], ip = #v, r, c=0); while(1, r = (n-(v[1]*v[2])) / (v[1]+v[2]); if(r < v[2], ip--, ip = #v; if(1==denominator(r) && isprime(r),c++)); if(!ip, return(c)); v[ip] = nextprime(1+v[ip]); for(i=1+ip,#v,v[i]=v[i-1])));
A369460(n) = A369054((12*n)-9);

Formula

a(n) = A369055((3*n)-2).