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URL: https://oeis.org/A239490

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A239490
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.
1
4, 27, 256, 1728, 2401, 3125, 11664, 72000, 78732, 200000, 486000, 531441, 823543, 1350000, 3280500, 9112500, 22143375, 52706752, 56250000, 61509375, 156250000
OFFSET
1,1
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
Sequence in context: A239298 A239299 A239300 * A239491 A365095 A324804
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Mar 20 2014
EXTENSIONS
a(15)-a(21) from Giovanni Resta, Mar 20 2014
STATUS
approved