A217856 Numbers with three prime factors, not necessarily distinct, except cubes of primes.

12, 18, 20, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244, 245, 246

Offset

1,1

Comments

Union of A007304 and A054753.

If n belongs to the sequence, then it can written n=pqr where p, q, r are primes and possibly two, but not all three of them are equal. It is named A3 in the link.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Wushi Goldring, Dynamics of the w function and primes, Journal of Number Theory, Volume 119, Issue 1, July 2006, Pages 86-98.

Example

12 = 2^2 * 3 = 2 * 2 * 3, and so it is in the sequence.
27 = 3^3 = 3 * 3 * 3, but that's only one distinct prime and hence 27 is not in the sequence.
30 = 2 * 3 * 5, and so it is in the sequence.

Mathematica

Select[Range[300], PrimeOmega[#] == 3 && PrimeNu[#] > 1 &] (* Alonso del Arte, Oct 14 2012 *)

Prog

(PARI) atr(n) = {for (i=2, n, if (bigomega(i) == 3 && omega(i) > 1, print1(i, ", "); ); ); }
(PARI) atr(n) = {for (i=2, n, f = factor(i); len = length(f~); if (len > 1, s = sum(i=1, len, f[i, 2]); if (s == 3, print1(i, ", "))); ); }

Crossrefs

Cf. A217857.

Sequence in context: A181595 A263189 A263838 * A253388 A030515 A162947

Adjacent sequences: A217853 A217854 A217855 * A217857 A217858 A217859

Keyword

nonn,easy

Author

Michel Marcus, Oct 13 2012

Status

approved