

A217856


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 8698.


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



