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A114636
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Numbers n such that n-th octagonal number is 8-almost prime.
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2
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22, 70, 80, 84, 102, 108, 118, 126, 134, 160, 174, 184, 200, 230, 240, 250, 252, 262, 264, 272, 318, 330, 334, 336, 350
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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n such that n*(3*n-2) has exactly eight prime factors (with multiplicity). n such that A000567(n) is an element of A046310. n such that A001222(A000567(n)) = 8. n such that A001222(n) + A001222(3*n-2) = 8. 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
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a(1) = 22 because OctagonalNumber(22) = Oct(22) = 22*(3*22-2) = 1408 = 2^7 * 11 has exactly 8 prime factors (seven are all equally 2; factors need not be distinct).
a(2) = 70 because Oct(70) = 70*(3*70-2) = 14560 = 2^5 * 5 * 7 * 13 is 8-almost prime.
a(3) = 80 because Oct(80) = 80*(3*80-2) = 19040 = 2^5 * 5 * 7 * 17.
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MATHEMATICA
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Select[Range[400], PrimeOmega[PolygonalNumber[8, #]]==8&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2020 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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