A380168 Nonsquares whose square part is greater than their squarefree part.

8, 12, 18, 27, 32, 45, 48, 50, 54, 63, 72, 75, 80, 96, 98, 108, 112, 125, 128, 147, 150, 160, 162, 175, 176, 180, 192, 200, 208, 216, 224, 240, 242, 243, 245, 250, 252, 275, 288, 294, 300, 320, 325, 338, 343, 350, 360, 363, 375, 384, 392, 396, 405, 425, 432, 448

Offset: 1

Author

Felix Huber, Jan 25 2025

Keywords

• nonn

Comments

Numbers A000037(k) for which A007913(A000037(k)) < A008833(A000037(k)).

Examples

			8 is in the sequence because its square part is 4 and its squarefree part is 2.
150 is in the sequence because its square part is 25 and its squarefree part is 6.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000037, A000290, A007913, A008833, A056623.

Programs

Maple

A380168:=proc(n)
    option remember;
    local a,r,i;
    if n=1 then
        8
    else
        for a from procname(n-1)+1 do
            r:=1;
            for i in ifactors(a)[2] do
                if is(i[2],odd) then
                    r:=r*i[1]
                fi
            od;
            if r>1 and rA380168(n),n=1..56);

PARI

select(x->(x>sqr(core(x))), select(x->(!issquare(x)), [1..500])) \\ Michel Marcus, Feb 10 2025