A239491 - OEIS

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

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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

AUTHOR

Paolo P. Lava, Mar 20 2014

EXTENSIONS

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

STATUS

approved