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A213420 Smallest number k such that the sum of prime factors of k (counted with multiplicity) is n times a square > 1. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 31 12:31 EST 2023. Contains 359971 sequences. (Running on oeis4.)