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A360769
Odd numbers that are neither prime powers nor squarefree.
5
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, 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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 28 2023
STATUS
approved