A324600 a(n) = (k(n)*(k(n) + 1))/2 with k = A018252 (nonprime numbers), for n >= 1.

1, 10, 21, 36, 45, 55, 78, 105, 120, 136, 171, 210, 231, 253, 300, 325, 351, 378, 406, 465, 528, 561, 595, 630, 666, 741, 780, 820, 903, 990, 1035, 1081, 1176, 1225, 1275, 1326, 1378, 1485, 1540, 1596, 1653, 1711, 1830, 1953, 2016, 2080, 2145, 2211, 2346, 2415, 2485, 2628, 2775, 2850, 2926, 3003, 3081, 3240, 3321, 3403, 3570, 3655, 3741, 3828, 3916

Offset: 1

Author

Wolfdieter Lang, Jul 10 2019

Keywords

• nonn
• easy

Comments

This is a proper subsequence of the triangular numbers A000217.

The infinite sum of the reciprocals is given in A307379 (which motivated this entry).

Crossrefs

Cf. A000217, A018252, A034953 (for prime numbers).

Programs

Magma

v:=[m:m in [1..500]| not IsPrime(m)];[v[k]*(v[k]+1)/2:k in [1..65]]; // Marius A. Burtea, Jul 12 2019

Magma

[n*(n+1)/2 : n in [1..100] | not IsPrime(n)]; // Vincenzo Librandi, Jul 12 2019

PARI

apply(x->x*(x+1)/2, select(x->!isprime(x), [1..90])) \\ Michel Marcus, Sep 18 2023

Formula

a(n) = A000217(A018252(n)), for n >= 1.