A163631 Partial sums of the odd nonprimes, A014076.

1, 10, 25, 46, 71, 98, 131, 166, 205, 250, 299, 350, 405, 462, 525, 590, 659, 734, 811, 892, 977, 1064, 1155, 1248, 1343, 1442, 1547, 1658, 1773, 1890, 2009, 2130, 2253, 2378, 2507, 2640, 2775, 2916, 3059, 3204, 3351, 3504, 3659, 3818, 3979, 4144, 4313

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 02 2009, Oct 10 2009

Keywords

• nonn

Comments

All entries besides the first are of the form 2+(k+1)^2-A007504(j), e.g., 10=2+25-17, 25=2+64-41, where the square is the sum of all odd numbers up to 1+2*k, and the 2 and A007504 represent the partial sum over the primes.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A014076.

Programs

Mathematica

upto=200; Accumulate[Complement[Range[1,upto,2], Prime[Range[2,PrimePi[upto]]]]] (* Harvey P. Dale, Mar 19 2011 *)

PARI

lista(nn) = {my(s = 0); forstep (n=1, nn, 2, if (!isprime(n), s+= n; print1(s, ", ")););} \\ Michel Marcus, Aug 01 2017

Formula

a(n) = Sum_{x= 1st odd nonprime..n-th odd nonprime}x.

Extensions

150 replaced with 250 by R. J. Mathar, Aug 06 2009