A213420 Smallest number k such that the sum of prime factors of k (counted with multiplicity) is n times a square > 1.

4, 15, 35, 39, 51, 95, 115, 87, 155, 111, 123, 215, 235, 159, 371, 183, 302, 335, 219, 511, 395, 415, 267, 623, 291, 303, 482, 327, 339, 791, 554, 1415, 635, 655, 411, 695, 662, 447, 698, 471, 734, 815, 835, 519, 1211, 543, 842, 1991, 579, 591, 914, 2167, 2587

Offset

1,1

Comments

Smallest k such that sopfr(k) = n*q^2.

a(n) = A213386(n), except for n = 1, 105, 173, 213, 227, 287, …

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(105) = 3764 because 3764 = 2^2 * 941 and  the sum of prime factors  (counted with multiplicity) is 4 + 941 = 945 = 105*9 where 9 is a square.

Maple

with(numtheory):
sopfr:= proc(n) option remember;
add(i[1]*i[2], i=ifactors(n)[2])
end:
a:= proc(n) local k, p;
for k from 2 while irem(sopfr(k), n, 'p')>0 or
sqrt(p)<>floor(sqrt(p)) or p=1 do od; k
end:
seq (a(n), n=1..100);

Crossrefs

Cf. A213386, A212401.

Sequence in context: A054556 A113693 A211537 * A209345 A323452 A330204

Adjacent sequences: A213417 A213418 A213419 * A213421 A213422 A213423

Keyword

nonn

Author

Michel Lagneau, Jun 11 2012

Status

approved