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A352997
Numbers k such that A352996(k) is prime.
3
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Apr 14 2022
STATUS
approved