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

1,7

Comments

See A369450 for the cumulative sum, and comments there.

Links

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

Formula

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

Prog

(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);

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.

Sequence in context: A194329 A321749 A143842 * A092876 A187360 A334368

Adjacent sequences: A369457 A369458 A369459 * A369461 A369462 A369463

Keyword

nonn

Author

Antti Karttunen, Jan 23 2024

Status

approved