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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 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

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Last modified May 29 21:28 EDT 2017. Contains 287257 sequences.