A229511 Numbers k whose arithmetic derivative (k') is a triangular number.

0, 1, 2, 3, 5, 7, 9, 11, 13, 17, 18, 19, 21, 23, 25, 26, 29, 31, 37, 38, 41, 43, 47, 50, 53, 59, 61, 67, 71, 73, 75, 79, 83, 86, 89, 97, 101, 102, 103, 106, 107, 109, 113, 115, 116, 127, 131, 137, 139, 147, 149, 151, 155, 157, 163, 167, 173, 178, 179, 181, 187, 191, 193, 197, 199

Offset

0,3

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Example

3 is in the sequence since 3'=1 and 1 is a triangular number.
4 is not in the sequence since 4'=4 and 4 is not a triangular number.

Maple

with(numtheory); P:= proc(q) local a, p, n;
for n from 0 to q do a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
if type((-1+sqrt(1+8*a))/2, integer) then print(n); fi; od; end: P(10^6); # Paolo P. Lava, Sep 25 2013

Crossrefs

Cf. A000217, A003415.

Sequence in context: A097046 A248420 A011861 * A305078 A328336 A337694

Adjacent sequences: A229508 A229509 A229510 * A229512 A229513 A229514

Keyword

nonn,easy

Author

Luca Brigada Villa, Sep 25 2013

Status

approved