A352990 Numbers k such that the k-th triangular number == 1 mod the integer log of k.

2, 6, 12, 21, 33, 45, 52, 63, 136, 162, 201, 205, 208, 225, 245, 253, 301, 304, 344, 441, 494, 531, 550, 637, 697, 720, 742, 806, 901, 910, 918, 1078, 1233, 1242, 1274, 1333, 1376, 1540, 1566, 1573, 1625, 1680, 1695, 1792, 1863, 1909, 2025, 2041, 2107, 2295, 2466, 2497, 2774, 2896, 2926, 2965

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 13 2022

Keywords

• nonn

Comments

Numbers k such that A000217(k) == 1 (mod A001414(k)).

Examples

			a(3) = 12 = 2*2*3 is a term because 12*13/2 = 78 == 1 (mod 2+2+3 = 7).
		

Links

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

Crossrefs

Cf. A000217, A001414, A352989.

Programs

Maple

filter:= proc(n) local t; (n*(n+1)/2) mod add(t[1]*t[2],t=ifactors(n)[2]) = 1 end proc:
select(filter, [$2..3000]);

Mathematica

Select[Range[3000], Mod[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] == 1 &] (* Amiram Eldar, Apr 14 2022 *)