A352989 Composites k such that the k-th triangular number is divisible by the integer log of k.

8, 15, 16, 27, 44, 54, 72, 84, 90, 95, 105, 125, 143, 150, 180, 195, 231, 256, 264, 287, 288, 308, 315, 319, 328, 351, 390, 423, 440, 483, 495, 512, 528, 540, 558, 559, 560, 576, 588, 608, 624, 627, 645, 648, 650, 728, 800, 805, 819, 840, 855, 870, 884, 896, 897, 924, 935, 945, 960, 975, 987

Offset: 1

Author

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

Keywords

• nonn

Comments

Composites k such that A000217(k) is divisible by A001414(k).

Contains all odd members of A046346, and in particular p^(p^k) if p is an odd prime and k >= 1.

Examples

			a(5) = 44 = 2*2*11 is a term because it is composite and A000217(44) = 44*45/2 = 990 is divisible by 2+2+11 = 15.
		

Links

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

Crossrefs

Cf. A000217, A001414, A046346.

Programs

Maple

filter:= proc(n) local t; not isprime(n) and (n*(n+1)/2/add(t[1]*t[2],t=ifactors(n)[2]))::integer end proc:
select(filter, [$4..1000]);

Mathematica

Select[Range[1000], CompositeQ[#] && Divisible[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] &] (* Amiram Eldar, Apr 13 2022 *)