A369057 Total number of representations of natural numbers in range 1 .. 4n-1 as sums of the form p*q + p*r + q*r, with three odd primes p <= q <= r.

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 7, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 14, 15, 15, 16, 17, 17, 17, 19, 21, 22, 22, 22, 24, 24, 24, 24, 25, 26, 28, 30, 31, 32, 32, 33, 35, 35, 35, 35, 38, 38, 39, 39, 41, 42, 44, 44, 47, 48, 49, 50, 50, 50, 51, 52, 52, 54, 54, 54, 59, 61, 61, 61, 63, 64, 65, 65, 67

Offset: 1

Author

Antti Karttunen, Jan 21 2024

Keywords

• nonn

Comments

Terms a(10^n), for n=1..7 are: 2, 82, 1819, 34220, 628914, 11855507, 233030075, which gives a(n)/n ratios: 0.2, 0.82, 1.82, 3.42, 6.29, 11.86, 23.30, etc, Question: does the ratio just keep on growing?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Partial sums of A369055.

Cf. A369054.

Programs

PARI

\\ Needs also program from A369055:
A369057list(up_to) = { my(v=vector(up_to)); s = 0; for(n=1,up_to,s+=A369055(n); v[n] = s); (v); };
v369057 = A369057list(up_to);
A369057(n) = v369057[n];