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A110226
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1 + sum of first n 4-almost primes.
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2
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1, 17, 41, 77, 117, 171, 227, 287, 368, 452, 540, 630, 730, 834, 960, 1092, 1227, 1363, 1503, 1653, 1805, 1961, 2145, 2334, 2530, 2728, 2932, 3142, 3362, 3587, 3815, 4047, 4281, 4529, 4779, 5039, 5315, 5609, 5905, 6202, 6508, 6816, 7131, 7459, 7789, 8129
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OFFSET
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0,2
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COMMENTS
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First differences are the sequence of 4-almost primes (A014613). Hence a(n) is the least positive sequence whose first differences are the sequence of 4-almost primes. Primes in this sequence include: a(1) = 17, a(2) = 41, a(6) = 227, a(35) = 5039, a(43) = 7459, a(44) = 7789. Semiprimes in this sequence include: a(3) = 77 = 7 * 11, a(7) = 287 = 7 * 41, a(16) = 1227 = 3 * 409, a(17) = 1363 = 29 * 47, a(21) = 1961 = 37 * 53, a(27) = 3142 = 2 * 1571, a(29) = 3587 = 17 * 211, a(32) = 4281 = 3 * 1427, a(33) = 4529 = 7 * 647, a(36) = 5315 = 5 * 1063, a(37) = 5609 = 71 * 79, a(38) = 5905 = 5 * 1181, a(42) = 7131 = 3 * 2733a(45) = 8129 = 11 * 739. 3-almost primes in this sequence include: a(4) = 117 = 3^2 * 13, a(5) = 171 = 3^2 * 19, a(9) = 452 = 2^2 * 113, a(12) = 730 = 2 * 5 * 73, a(13) = 833 = 2 * 3 * 139, a(18) = 3^2 * 167, a(19) = 1653 = 3 * 19 * 29, a(20) = 1805 = 5 * 19^2, a(23) = 2534 = 2 * 3 * 389, a(26) = 2932 = 2^2 * 733, a(28) = 3362 = 2 * 41^2, a(30) = 3815 = 5 * 7 * 109, a(31) = 4047 = 3 * 19 * 71, a(39) = 2 * 7 * 443, a(40) = 6508 = 2^2 * 1627. 4-almost primes in this sequence include: a(22) = 2145 = 3 * 5 * 11 * 13, a(24) = 2530 = 2 * 5 * 11 * 23.
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LINKS
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FORMULA
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a(0) = 1; for n>0, a(n) = 1 + A086046(n).
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MATHEMATICA
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Accumulate[Join[{1}, Select[Range[500], PrimeOmega[#]==4&]]] (* Harvey P. Dale, Dec 13 2018 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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