A229511 - OEIS

%I #12 Apr 27 2019 02:33:06

%S 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,

%T 59,61,67,71,73,75,79,83,86,89,97,101,102,103,106,107,109,113,115,116,

%U 127,131,137,139,147,149,151,155,157,163,167,173,178,179,181,187,191,193,197,199

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

%H Paolo P. Lava, <a href="/A229511/b229511.txt">Table of n, a(n) for n = 0..1000</a>

%e 3 is in the sequence since 3'=1 and 1 is a triangular number.

%e 4 is not in the sequence since 4'=4 and 4 is not a triangular number.

%p with(numtheory); P:= proc(q) local a,p,n;

%p for n from 0 to q do a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);

%p if type((-1+sqrt(1+8*a))/2,integer) then print(n); fi; od; end: P(10^6); # _Paolo P. Lava_, Sep 25 2013

%Y Cf. A000217, A003415.

%K nonn,easy

%O 0,3

%A _Luca Brigada Villa_, Sep 25 2013