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A114621 Numbers n such that n-th octagonal number is 5-almost prime. 1
8, 10, 12, 20, 26, 28, 45, 58, 63, 68, 76, 81, 82, 92, 99, 106, 115, 116, 129, 146, 159, 165, 171, 172, 188, 195, 202, 212, 213, 218, 225, 236, 255, 259, 261, 268, 273, 279, 298, 309, 325, 339, 343, 351, 362, 375, 387, 395, 399 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), or 4-almost prime (A014613).

LINKS

Table of n, a(n) for n=1..49.

Eric Weisstein's World of Mathematics, Octagonal Number.

Eric Weisstein's World of Mathematics, Almost Prime.

FORMULA

n such that n*(3*n-2) has exactly five prime factors (with multiplicity). n such that A000567(n) is an element of A014614. n such that A001222(A000567(n)) = 5. n such that A001222(n) + A001222(3*n-2) = 5. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014614.

EXAMPLE

a(1) = 8 because OctagonalNumber(8) = Oct(8) = 8*(3*8-2) = 176 = 2^4 * 11 has exactly 5 prime factors (four are all equally 2; factors need not be distinct). Also, 176 = Oct(8) = Oct(Oct(2)), an iterated octagonal number. Also, 176 is a pengaonal number, hence an element of A046189 octagonal pentagonal numbers.

a(2) = 10 because Oct(10) = 10*(3*10-2) = 280 = 2^3 * 5 * 7 is 5-almost prime.

a(4) = 20 because Oct(20) = 20*(3*20-2) = 1160 = 2^3 * 5 * 29.

a(5) = 26 because Oct(26) = 26*(3*26-2) = 1976 = 2^3 * 13 * 19.

a(19) = 129 because Oct(129) = 129*(3*129-2) = 49665 = 3 * 5 * 7 * 11 * 43 is 5-almost prime (in this case, the 5 prime factors are distinct).

CROSSREFS

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614.

Sequence in context: A208154 A096281 A114873 * A174156 A115168 A303223

Adjacent sequences:  A114618 A114619 A114620 * A114622 A114623 A114624

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 17 2006

EXTENSIONS

12, 63, 99 inserted and 117 removed by R. J. Mathar, Dec 22 2010

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)