

A110226


1 + sum of first n 4almost primes.


2



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

0,2


COMMENTS

First differences are the sequence of 4almost primes (A014613). Hence a(n) is the least positive sequence whose first differences are the sequence of 4almost 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. 3almost 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. 4almost primes in this sequence include: a(22) = 2145 = 3 * 5 * 11 * 13, a(24) = 2530 = 2 * 5 * 11 * 23.


LINKS

Table of n, a(n) for n=0..45.


FORMULA

a(0) = 1; for n>0, a(n) = 1 + A086046(n).


MATHEMATICA

Accumulate[Join[{1}, Select[Range[500], PrimeOmega[#]==4&]]] (* Harvey P. Dale, Dec 13 2018 *)


CROSSREFS

Cf. A014613, A086046, A110208, A110209.
Sequence in context: A166147 A028886 A146443 * A054819 A235743 A299797
Adjacent sequences: A110223 A110224 A110225 * A110227 A110228 A110229


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Sep 06 2005


STATUS

approved



