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

1,1

Comments

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

Links

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

Example

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.

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 r<a/r then
                return a
            fi
        od
    fi;
end proc;
seq(A380168(n), n=1..56);

Prog

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

Crossrefs

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

Sequence in context: A293529 A028393 A066681 * A276403 A171241 A386792

Adjacent sequences: A380165 A380166 A380167 * A380169 A380170 A380171

Keyword

nonn

Author

Felix Huber, Jan 25 2025

Status

approved