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Search: id:A114635
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| A114635 |
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Numbers n such that n-th octagonal number is 7-almost prime. |
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+0
2
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| 24, 30, 32, 38, 48, 66, 72, 78, 90, 94, 104, 110, 112, 114, 120, 136, 140, 154, 164, 166, 168, 176, 180, 190, 204, 206, 208, 210, 220, 222, 228, 238, 248, 254, 276, 280, 284, 286, 290, 300, 306, 312, 326, 338, 344
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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), or 6-almost prime (A046308).
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LINKS
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Eric Weisstein's World of Mathematics, Octagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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n such that n*(3*n-2) has exactly seven prime factors (with multiplicity). n such that A000567(n) is an element of A046308. n such that A001222(A000567(n)) = 7. n such that A001222(n) + A001222(3*n-2) = 7. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A046308.
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EXAMPLE
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a(1) = 24 because OctagonalNumber(24) = Oct(24) = 24*(3*24-2) = 96 = 1680 = 2^4 * 3 * 5 * 7 has exactly 7 prime factors (four are all equally 2; factors need not be distinct).
a(2) = 30 because Oct(30) = 30*(3*30-2) = 2640 = 2^4 * 3 * 5 * 11 is 7-almost prime.
a(3) = 32 because Oct(32) = 32*(3*32-2) = 3008 = 2^6 * 47 is 7-almost prime.
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CROSSREFS
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Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308.
Sequence in context: A093455 A080564 A048260 this_sequence A077969 A122181 A167758
Adjacent sequences: A114632 A114633 A114634 this_sequence A114636 A114637 A114638
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 18 2006
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