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A346041 Numbers with exactly 1 semiprime divisor. 6

%I #13 Jul 11 2021 12:38:50

%S 4,6,8,9,10,14,15,16,21,22,25,26,27,32,33,34,35,38,39,46,49,51,55,57,

%T 58,62,64,65,69,74,77,81,82,85,86,87,91,93,94,95,106,111,115,118,119,

%U 121,122,123,125,128,129,133,134,141,142,143,145,146,155,158,159,161,166,169

%N Numbers with exactly 1 semiprime divisor.

%C Numbers of the form p*q or p^k, where p and q are prime and k >= 2.

%e 6 is in the sequence since it has exactly 1 semiprime divisor, 6.

%e 16 is in the sequence since it has exactly 1 semiprime divisor, 4.

%t Select[Range@200,Length@Select[Divisors@#,PrimeOmega@#==2&]==1&] (* _Giorgos Kalogeropoulos_, Jul 03 2021 *)

%o (PARI) isok(k) = sumdiv(k, d, bigomega(d)==2) == 1; \\ _Michel Marcus_, Jul 03 2021

%o (Python)

%o from sympy import factorint

%o def ok(n):

%o f = factorint(n); w = len(f); W = sum(f.values())

%o return (w == 1 and W >= 2) or (w == 2 and W == 2)

%o print(list(filter(ok, range(170)))) # _Michael S. Branicky_, Jul 03 2021

%Y Cf. A001358 (semiprimes), A086971.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 02 2021

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