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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000217, A001414, A046346.

Sequence in context: A229839 A114605 A300860 * A367335 A369497 A031103

Adjacent sequences: A352986 A352987 A352988 * A352990 A352991 A352992

Keyword

nonn

Author

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

Status

approved