A291167 Numbers k such that psi(k) is a perfect square where psi(k) = A001615(k).

1, 3, 18, 20, 22, 27, 60, 66, 70, 72, 80, 88, 92, 94, 99, 115, 119, 162, 170, 210, 212, 214, 217, 240, 243, 252, 264, 265, 276, 280, 282, 288, 308, 310, 315, 320, 322, 345, 352, 357, 368, 376, 382, 385, 423, 497, 500, 510, 517, 527, 540, 594, 596, 612, 636, 637, 642, 648, 651, 679, 680, 710, 725, 742

Offset

1,2

Comments

The product of an even number of distinct members of A066436 is in the sequence. - Robert Israel, Aug 22 2017

Links

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

Example

60 is a term because psi(60) = 144 is a perfect square.

Maple

filter:= proc(n) issqr(n*mul(1+1/p, p=numtheory:-factorset(n))) end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 22 2017

Mathematica

Select[Range@ 750, IntegerQ@ Sqrt[# Sum[MoebiusMu[d]^2/d, {d, Divisors@ #}]] &] (* Michael De Vlieger, Aug 19 2017 *)

Prog

(PARI) a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);
is(n) = issquare(a001615(n));

Crossrefs

Cf. A001615, A006532, A066436.

Sequence in context: A307640 A339631 A195998 * A361592 A174029 A103715

Adjacent sequences: A291164 A291165 A291166 * A291168 A291169 A291170

Keyword

nonn,easy

Author

Altug Alkan, Aug 19 2017

Status

approved