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A114437
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Indices of 6-almost prime triangular numbers.
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0
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32, 48, 96, 99, 104, 111, 119, 120, 125, 152, 161, 168, 176, 188, 189, 195, 200, 208, 223, 231, 239, 240, 252, 260, 264, 275, 299, 300, 303, 304, 315, 336, 342, 343, 344, 352, 359, 363, 374, 377, 391, 392, 395, 400
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..44.
Eric Weisstein's World of Mathematics, Triangular Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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{a(n)} = {k such that A001222(A000217(k)) = 6}. {a(n)} = {k such that k*(k+1)/2 has exactly 6 prime factors, with multiplicity}. {a(n)} = {k such that A000217(k) is an element of A046306}.
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EXAMPLE
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a(1) = 48 because T(48) = TriangularNumber(48) = 48*(48+1)/2 = 1176 = 2^3 * 3 * 7^2 is a 6-almost prime.
a(2) = 96 because T(96) = 96*(96+1)/2 = 4656 = 2^4 * 3 * 97 is a 6-almost prime.
a(18) = 200 because T(200) = 200*(200+1)/2 = 20100 = 2^2 * 3 * 5^2 * 67 is a 6-almost prime.
a(29) = 300 because T(300) = 300*(300+1)/2 = 45150 = 2 * 3 * 5^2 * 7 * 43 is a 6-almost prime.
a(38) = 363 because T(363) = 363*(363+1)/2 = 45150 = 66066 = 2 * 3 * 7 * 11^2 * 13 is a 6-almost prime (363 and 66066 are both palindromatic).
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MATHEMATICA
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Select[Range[400], PrimeOmega[(#(#+1))/2]==6&] (* From Harvey P. Dale, Mar 29 2012 *)
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PROG
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(PARI) isA114437(n)=bigomega(n*(n+1)/2)==6 /* Michael B. Porter, Mar 30 2012 */
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CROSSREFS
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Cf. A000217, A001222, A046306.
Sequence in context: A014614 A046371 A175162 * A039379 A043202 A043982
Adjacent sequences: A114434 A114435 A114436 * A114438 A114439 A114440
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Feb 14 2006
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EXTENSIONS
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Corrected by Harvey P. Dale, Mar 29 2012
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STATUS
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approved
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