A297401 Non-sphenic numbers with exactly 8 divisors.

24, 40, 54, 56, 88, 104, 128, 135, 136, 152, 184, 189, 232, 248, 250, 296, 297, 328, 344, 351, 375, 376, 424, 459, 472, 488, 513, 536, 568, 584, 621, 632, 664, 686, 712, 776, 783, 808, 824, 837, 856, 872, 875, 904, 999, 1016, 1029, 1048, 1096, 1107, 1112, 1161, 1192

Offset

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Caldwell and Honaker, Prime Curios!

Wikipedia, Sphenic number

Formula

Equals {A030626} \ {A007304}. - Omar E. Pol, Dec 30 2017

Maple

N:= 1000: # to get all terms <= N
P:= select(isprime, [2, seq(i, i=3..N)]):
R:= NULL:
for p in P do
  if p^7 <= N then R:= R, p^7 fi;
  if p^3 > N then break fi;
  for q in P while p^3*q <= N do if q <> p then R:= R, p^3*q fi od:
od:
sort([R]); # Robert Israel, Dec 31 2017

Mathematica

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

Prog

(PARI) isok(n) = !((bigomega(n)==3) && (omega(n)==3)) && (numdiv(n) == 8); \\ Michel Marcus, Dec 29 2017

Crossrefs

Subsequence of A030626.

Cf. A000005, A030626, A065036, A092759.

Sequence in context: A334801 A362594 A360793 * A065127 A065036 A329880

Adjacent sequences: A297398 A297399 A297400 * A297402 A297403 A297404

Keyword

nonn

Author

G. L. Honaker, Jr., Dec 29 2017

Extensions

More terms from Michel Marcus, Dec 29 2017

Status

approved