A261887 Number of triples of primes (p,q,r) that satisfy p+q^2+r^3=n.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 3, 1, 2, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 2, 3, 3, 1, 1, 1, 4, 3, 0, 3, 1, 3, 3, 0, 1, 2, 1, 3, 2, 1, 2, 3, 1, 3, 1, 3, 3, 2, 2, 0, 4, 2, 1, 2, 1, 2, 3, 2
Offset: 1
Keywords
Examples
For p=2, p+p^2+p^3 = 14 = A181149(1), so a(14)=1.
Links
- Ana Rechtman, Août 2015, 4e défi, Images des Mathématiques, CNRS, 2015.
Programs
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PARI
a(n) = {nb = 0; forprime(p=2, n, forprime(q=2, n, if (p+q^2 > n, break); forprime(r=2, n, if (p+q^2+r^3 > n, break); if (p+q^2+r^3 == n, nb++);););); nb;}
Formula
G.f.: (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(prime(j)^2))*(Sum_{k>=1} x^(prime(k)^3)). - Ilya Gutkovskiy, Feb 06 2017