

A069277


16almost primes (generalization of semiprimes).


27



65536, 98304, 147456, 163840, 221184, 229376, 245760, 331776, 344064, 360448, 368640, 409600, 425984, 497664, 516096, 540672, 552960, 557056, 573440, 614400, 622592, 638976, 746496, 753664, 774144, 802816, 811008, 829440, 835584, 860160
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OFFSET

1,1


COMMENTS

Product of 16 not necessarily distinct primes.
Divisible by exactly 16 prime powers (not including 1).
Any 16almost prime can be represented in several ways as a product of two 8almost primes A046310; in several ways as a product of four 4almost primes A014613; and in several ways as a product of eight semiprimes A001358.  Jonathan Vos Post, Dec 12 2004


LINKS

D. W. Wilson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

Product p_i^e_i with Sum e_i = 16.


MATHEMATICA

Select[Range[300000], Plus @@ Last /@ FactorInteger[ # ] == 16 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[10^6], PrimeOmega[#]==16&] (* Harvey P. Dale, Jan 30 2015 *)


PROG

(PARI) k=16; start=2^k; finish=1000000; v=[] for(n=start, finish, if(bigomega(n)==k, v=concat(v, n))); v


CROSSREFS

Cf. A014610, A101637, A101638, A101605, A101606.
Sequences listing ralmost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), this sequence (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20).  Jason Kimberley, Oct 02 2011
Sequence in context: A223602 A223695 A202939 * A202932 A258737 A255667
Adjacent sequences: A069274 A069275 A069276 * A069278 A069279 A069280


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Mar 13 2002


STATUS

approved



