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%I #18 Apr 19 2022 09:24:28
%S 4,9,18,20,24,25,30,42,49,50,57,65,66,69,70,75,76,78,80,85,93,96,98,
%T 99,102,104,110,112,114,121,129,133,141,145,152,153,169,177,186,189,
%U 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
%N Numbers k such that A352996(k) is prime.
%C Numbers k such that the k-th triangular number mod the sum (with multiplicity) of prime factors of k is prime.
%C Contains p^2 for prime p.
%H Robert Israel, <a href="/A352997/b352997.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 18 is a term because A352996(18) = A000217(18) mod A001414(18) = 171 mod 8 = 3 is prime.
%p filter:= proc(n) local t; isprime((n*(n+1)/2) mod add(t[1]*t[2],t=ifactors(n)[2])) end proc:
%p select(filter, [$2..500]);
%t Select[Range[300], PrimeQ[Mod[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]]] &] (* _Amiram Eldar_, Apr 14 2022 *)
%Y Cf. A000217, A001414, A352996.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Apr 14 2022