A324600 - OEIS

%I #18 Sep 18 2023 09:01:02

%S 1,10,21,36,45,55,78,105,120,136,171,210,231,253,300,325,351,378,406,

%T 465,528,561,595,630,666,741,780,820,903,990,1035,1081,1176,1225,1275,

%U 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

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

%C This is a proper subsequence of the triangular numbers A000217.

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

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

%o (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

%o (Magma) [n*(n+1)/2 : n in [1..100] | not IsPrime(n)]; // _Vincenzo Librandi_, Jul 12 2019

%o (PARI) apply(x->x*(x+1)/2, select(x->!isprime(x), [1..90])) \\ _Michel Marcus_, Sep 18 2023

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

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Jul 10 2019