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A114828
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Numbers n such that n-th octagonal number is 9-almost prime.
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0
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64, 96, 128, 144, 162, 182, 198, 216, 224, 234, 246, 270, 278, 288, 304, 310, 320, 324, 352, 390, 414, 416, 432, 438, 480, 504, 528, 544, 550, 558, 584, 594, 600, 646, 648, 654, 662, 684, 694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), 4-almost prime (A014613), 5-almost prime (A014614), 6-almost prime (A046306), 7-almost prime (A046308), or 8-almost prime (A046310).
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LINKS
| Eric Weisstein's World of Mathematics, Octagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
| n such that n*(3*n-2) has exactly nine prime factors (with multiplicity). n such that A000567(n) is an element of A046312. n such that A001222(A000567(n)) = 9. n such that A001222(n) + A001222(3*n-2) = 9. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A046310.
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EXAMPLE
| a(1) = 64 because OctagonalNumber(64) = Oct(64) = 64*(3*64-2) = 12160 = 2^7 * 5 * 19 has exactly 9 prime factors (seven are all equally 2; factors need not be distinct).
a(2) = 96 because Oct(96) = 96*(3*96-2) = 27456 = 2^6 * 3 * 11 * 13 is 9-almost prime [also 27456 = Oct(96) = Oct(Oct(6)) is an iterated octagonal number].
a(3) = 128 because Oct(128) = 128*(3*128-2) = 48896 = 2^8 * 191.
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PROG
| (MAGMA) A000567:=func< n | n*(3*n-2) >; Is9almostprime:=func< n | &+[k[2]: k in Factorization(n)] eq 9 >; [ n: n in [2..1000] | Is9almostprime(A000567(n)) ]; // Klaus Brockhaus, Dec 22 2010
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CROSSREFS
| Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308, A046310, A046312, A088878, A114606, A114618, A114621, A114634, A114635, A114636.
Sequence in context: A114407 A114417 A046305 * A036330 A046306 A175163
Adjacent sequences: A114825 A114826 A114827 * A114829 A114830 A114831
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006
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EXTENSIONS
| Missing terms inserted - R. J. Mathar, Dec 22 2010
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