%I #49 Apr 03 2023 10:36:13

%S 24,40,54,56,88,104,128,135,136,152,184,189,232,248,250,296,297,328,

%T 344,351,375,376,424,459,472,488,513,536,568,584,621,632,664,686,712,

%U 776,783,808,824,837,856,872,875,904,999,1016,1029,1048,1096,1107,1112,1161,1192

%N Non-sphenic numbers with exactly 8 divisors.

%C These are the numbers of the form p^3*q (with primes p and q distinct) or p^7. Thus it is the union of A065036 and A092759, and this can be used for direct enumeration. - _Alex Meiburg_, Dec 31 2017

%H Robert Israel, <a href="/A297401/b297401.txt">Table of n, a(n) for n = 1..10000</a>

%H Caldwell and Honaker, <a href="https://t5k.org/curios/page.php?curio_id=31757">Prime Curios!</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sphenic_number">Sphenic number</a>

%F Equals {A030626} \ {A007304}. - _Omar E. Pol_, Dec 30 2017

%p N:= 1000: # to get all terms <= N

%p P:= select(isprime, [2,seq(i,i=3..N)]):

%p R:= NULL:

%p for p in P do

%p if p^7 <= N then R:= R, p^7 fi;

%p if p^3 > N then break fi;

%p for q in P while p^3*q <= N do if q <> p then R:= R, p^3*q fi od:

%p od:

%p sort([R]); # _Robert Israel_, Dec 31 2017

%t Select[Range@ 1200, And[DivisorSigma[0, #] == 8, Nand[PrimeNu[#] == 3, PrimeOmega[#] == 3]] &] (* _Michael De Vlieger_, Dec 29 2017 *)

%o (PARI) isok(n) = !((bigomega(n)==3) && (omega(n)==3)) && (numdiv(n) == 8); \\ _Michel Marcus_, Dec 29 2017

%Y Subsequence of A030626.

%Y Cf. A000005, A030626, A065036, A092759.

%K nonn

%O 1,1

%A _G. L. Honaker, Jr._, Dec 29 2017

%E More terms from _Michel Marcus_, Dec 29 2017