A072327 Numbers k such that k^2 is a term of A072510.

1, 8, 12, 27, 32, 45, 63, 125, 175, 225, 243, 275, 325, 343, 425, 475, 539, 560, 575, 637, 720, 833, 931, 1127, 1225, 1331, 1421, 1519, 1573, 1813, 2009, 2057, 2107, 2197, 2240, 2299, 2303, 2783, 2816, 2873, 3025, 3125, 3211, 3328, 3509, 3751, 3887, 4352, 4477

Offset

1,2

Comments

Numbers of the form p^(m*(4m-1)) and p^(m*(4m+1)) are terms of the sequence, where p is prime. p^2*q are terms of the sequence, where p and q are prime and p^2 > q > p.

Complement of A072497 in the positive integers. - Robert Israel, Dec 10 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) local s, F, d, p;
  s:= n^2;
  F:= sort(convert(numtheory:-divisors(s), list));
  p:= 1:
  for d in F do
    p:= p*d;
    if p > s then return false
    elif p = s then return true
    fi
  od;
end proc:
select(filter, [$1..5000]); # Robert Israel, Dec 10 2024

Crossrefs

Cf. A072497, A072498, A072510.

Sequence in context: A045523 A006983 A283148 * A218558 A181735 A161415

Adjacent sequences: A072324 A072325 A072326 * A072328 A072329 A072330

Keyword

nonn

Author

Vladimir Baltic, Aug 04 2002

Extensions

More terms from Sean A. Irvine, Sep 23 2024

Status

approved