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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A000217, A001414, A352996.

Sequence in context: A139468 A127081 A162719 * A313357 A313358 A263351

Adjacent sequences: A352994 A352995 A352996 * A352998 A352999 A353000

Keyword

nonn

Author

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

Status

approved