A239491 Numbers n such that Sum_{i=1..j} 1/pn(i) - Sum_{i=1..k} 1/pd(i) is an integer, where pn are the prime factors of n and pd the prime factors of the arithmetic derivative of n, both counted with multiplicity.

4, 27, 256, 1728, 3125, 11664, 78732, 200000, 531441, 823543, 1350000, 9112500, 52706752, 61509375, 156250000

Offset

1,1

Comments

Subset of A239490.

A051674 is a subset of this sequence.

Links

Table of n, a(n) for n=1..15.

Example

Arithmetic derivative of 1728 is 6912. Prime factors of 1728 are 2^6, 3^3; prime factors of 6912 are 2^8, 3^3 and 6*1/2 + 3*1/3 + 8*1/2 + 3*1/3 = 9.

Maple

with(numtheory); P:= proc(q) local a, b, c, n, p;
for n from 2 to q do a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
b:=ifactors(a)[2]; c:=ifactors(n)[2]; if type(add(c[k][2]/c[k][1], k=1..nops(c))-add(b[k][2]/b[k][1], k=1..nops(b)), integer) then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A003415, A239490.

Sequence in context: A239299 A239300 A239490 * A365095 A324804 A245409

Adjacent sequences: A239488 A239489 A239490 * A239492 A239493 A239494

Keyword

nonn,more,changed

Author

Paolo P. Lava, Mar 20 2014

Extensions

a(12)-a(15) from Giovanni Resta, Mar 20 2014

Status

approved