A352997 Numbers k such that A352996(k) is prime.

4, 9, 18, 20, 24, 25, 30, 42, 49, 50, 57, 65, 66, 69, 70, 75, 76, 78, 80, 85, 93, 96, 98, 99, 102, 104, 110, 112, 114, 121, 129, 133, 141, 145, 152, 153, 169, 177, 186, 189, 190, 192, 198, 213, 217, 228, 238, 242, 249, 252, 258, 261, 266, 272, 273, 275, 282, 286, 289, 290, 292, 294, 297, 305, 309

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 14 2022

Keywords

• nonn

Comments

Numbers k such that the k-th triangular number mod the sum (with multiplicity) of prime factors of k is prime.

Contains p^2 for prime p.

Examples

			a(3) = 18 is a term because A352996(18) = A000217(18) mod A001414(18) = 171 mod 8 = 3 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A001414, A352996.

Programs

Maple

filter:= proc(n) local t; isprime((n*(n+1)/2) mod add(t[1]*t[2],t=ifactors(n)[2])) end proc:
select(filter, [$2..500]);

Mathematica

Select[Range[300], PrimeQ[Mod[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]]] &] (* Amiram Eldar, Apr 14 2022 *)