A291167 - OEIS

%I #16 Jul 23 2021 02:08:25

%S 1,3,18,20,22,27,60,66,70,72,80,88,92,94,99,115,119,162,170,210,212,

%T 214,217,240,243,252,264,265,276,280,282,288,308,310,315,320,322,345,

%U 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

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

%C The product of an even number of distinct members of A066436 is in the sequence. - _Robert Israel_, Aug 22 2017

%H Robert Israel, <a href="/A291167/b291167.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) issqr(n*mul(1+1/p,p=numtheory:-factorset(n))) end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Aug 22 2017

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

%o (PARI) a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);

%o is(n) = issquare(a001615(n));

%Y Cf. A001615, A006532, A066436.

%K nonn,easy

%O 1,2

%A _Altug Alkan_, Aug 19 2017