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Search: id:A114606
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| A114606 |
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Numbers n such that n-th octagonal number is 3-almost prime. |
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2
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| 2, 15, 17, 19, 21, 25, 29, 31, 33, 35, 41, 51, 55, 65, 73, 77, 79, 83, 89, 91, 93, 95, 97, 101, 107, 111, 123, 131, 133, 139, 141, 145, 149, 151, 155, 157, 173, 179, 183, 197, 201, 203, 205, 215, 221, 223, 227, 229, 233, 237, 241, 247, 253
(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 either prime or semiprime.
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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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Numbers n such that n*(3*n-2) has exactly three prime factors (with multiplicity). n such that A000567(n) is an element of A014612. n such that A001222(A000567(n)) = 3. n such that A001222(n) + A001222(3*n-2) = 3. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014612.
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EXAMPLE
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a(1) = 2 because OctagonalNumber(2) = Oct(2) = 2*(3*2-2) = 8 = 2^3 has exactly three prime factors (which are all equally 2; factors need not be distinct).
a(2) = 15 because Oct(15) = 15*(3*15-2) = 645 = 3 * 5 * 43, a 3-almost prime.
a(5) = 21 because Oct(21) = 21*(3*21-2) = 1281 = 3 * 7 * 61 [also, 1281 = Oct(21) = Oct(Oct(3)) is an iterated octagonal number].
a(14) = 65 because Oct(65) = 65*(3*65-2) = 12545 = 5 * 13 * 193 [also, 12545 = Oct(65) = Oct(Oct(5)) is an iterated octagonal number].
a(29) = 133 because Oct(133) = 133*(3*133-2) = 52801 = 7 * 19 * 397 [also, 52801 = Oct(133) = Oct(Oct(7)) is an iterated octagonal number].
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CROSSREFS
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Cf. A000040, A000567, A001222, A014612.
Sequence in context: A108472 A039771 A032934 this_sequence A022117 A042571 A041797
Adjacent sequences: A114603 A114604 A114605 this_sequence A114607 A114608 A114609
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 17 2006
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