A213386 Smallest number k such that the sum of the distinct prime divisors of k equals n times a square > 1.

14, 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

Offset

1,1

Comments

Smallest k such that sopf(k) = n*q where q is a square.

Links

Michel Lagneau, Table of n, a(n) for n = 1..1000

Example

a(55) = 2631 because 2631 = 3*877 and 3 + 877 = 880 = 55*16 where 16 is a square.

Maple

with (numtheory):
sopf:= proc(n) option remember;
add(i, i=factorset(n))
end:
a:= proc(n) local k, p;
for k from 2 while irem(sopf(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. A008492, A213420.

Sequence in context: A162283 A180328 A211144 * A370403 A370405 A357625

Adjacent sequences: A213383 A213384 A213385 * A213387 A213388 A213389

Keyword

nonn

Author

Michel Lagneau, Jun 10 2012

Status

approved