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A114635 Numbers n such that n-th octagonal number is 7-almost prime. 1
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; 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), 4-almost prime (A014613), 5-almost prime (A014614), or 6-almost prime (A046308).

LINKS

Table of n, a(n) for n=1..45.

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 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.

EXAMPLE

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.

CROSSREFS

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308.

Sequence in context: A093455 A080564 A048260 * A077969 A122181 A167758

Adjacent sequences:  A114632 A114633 A114634 * A114636 A114637 A114638

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 18 2006

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)