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

Author

Michael De Vlieger, Feb 28 2023

Keywords

• nonn

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.

Crossrefs

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

Programs

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[#]] &]

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

Formula

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