A230544 Solutions of the equation k'' = tau(k) * k', where k' and k'' are the first and the second arithmetic derivative of k.

1, 1255, 4063, 5359, 6583, 8615, 11623, 12047, 14359, 14863, 15943, 27644, 32471, 49271, 52607, 81599, 98471, 101687, 117647, 164327, 173447, 176471, 203327, 209207, 235271, 246647, 277271, 301607, 343271, 355871, 358367, 360623, 378047, 392471, 401927, 406607

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Example

For k = 6583 we have tau(k) = 4, k' = 256, k'' = 1024 and 1024 = 4 * 256.

Maple

with(numtheory); P:= proc(q) local a1, a2, n, p;
for n from 1 to q do a1:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); ;
a2:=a1*add(op(2, p)/op(1, p), p=ifactors(a1)[2]);
if a2=tau(n)*a1 then print(n); fi; od; end: P(10^6);

Crossrefs

Cf. A000005, A003415, A068346.

Sequence in context: A023068 A062693 A067203 * A280928 A080718 A219993

Adjacent sequences: A230541 A230542 A230543 * A230545 A230546 A230547

Keyword

nonn

Author

Paolo P. Lava, Oct 25 2013

Status

approved