A360769 Odd numbers that are neither prime powers nor squarefree.

45, 63, 75, 99, 117, 135, 147, 153, 171, 175, 189, 207, 225, 245, 261, 275, 279, 297, 315, 325, 333, 351, 363, 369, 375, 387, 405, 423, 425, 441, 459, 475, 477, 495, 507, 513, 525, 531, 539, 549, 567, 575, 585, 603, 605, 621, 637, 639, 657, 675, 693, 711, 725, 735, 747, 765, 775, 783, 801, 819, 825

Offset

1,1

Comments

Odd numbers k such that A001222(k) > A001221(k) > 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, 2048 pixel square bitmap of n = 1..4194304, read left to right, top to bottom, showing odd A126706(n) in black.

Formula

a(n) = { A005408 INTERSECT A126706 } = intersection of A005418, A013929, and A024619.

Maple

filter:= proc(n) local F;
F:= ifactors(n)[2];
nops(F)>1 and max(F[.., 2]) > 1
end proc:
select(filter, [seq(i, i = 1 .. 1000, 2)]); # Robert Israel, Mar 01 2023

Mathematica

Select[Range[1, 825, 2], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]

Prog

(PARI) isok(k) = (k%2) && !isprimepower(k) && !issquarefree(k); \\ Michel Marcus, Feb 28 2023
(Python)
from itertools import count, islice
from sympy import factorint
def A360769_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: sum(f:=factorint(n).values()) > len(f) > 1, count(max(startvalue+(startvalue&1^1), 1), 2))
A360769_list = list(islice(A360769_gen(), 20)) # Chai Wah Wu, Mar 01 2023

Crossrefs

Cf. A001221, A001222, A005418, A013929, A024619, A126706.

Sequence in context: A230577 A336555 A175761 * A046364 A321498 A051773

Adjacent sequences: A360766 A360767 A360768 * A360770 A360771 A360772

Keyword

nonn

Author

Michael De Vlieger, Feb 28 2023

Status

approved