

A229511


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


2



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
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OFFSET

0,3


LINKS



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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



