A239490 Numbers n such that Sum_{i=1..j} 1/pn(i) + Sum_{i=1..k} 1/pd(i) is 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, 2401, 3125, 11664, 72000, 78732, 200000, 486000, 531441, 823543, 1350000, 3280500, 9112500, 22143375, 52706752, 56250000, 61509375, 156250000

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Example

Arithmetic derivative of 2401 is 1372. Prime factors of 2401 are 7^4; prime factors of 1372 are 2^2, 7^3 and 1/7 + 1/7 + 1/7 + 1/7 + 1/2 + 1/2 + 1/7 + 1/7 + 1/7 = 2.

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, A239491.

Sequence in context: A239298 A239299 A239300 * A239491 A365095 A324804

Adjacent sequences: A239487 A239488 A239489 * A239491 A239492 A239493

Keyword

nonn,more

Author

Paolo P. Lava, Mar 20 2014

Extensions

a(15)-a(21) from Giovanni Resta, Mar 20 2014

Status

approved