A110209 1 + sum of first n 3-almost primes.

1, 9, 21, 39, 59, 86, 114, 144, 186, 230, 275, 325, 377, 440, 506, 574, 644, 719, 795, 873, 965, 1063, 1162, 1264, 1369, 1479, 1593, 1709, 1826, 1950, 2075, 2205, 2343, 2490, 2638, 2791, 2945, 3109, 3274, 3444, 3615, 3787, 3961, 4136, 4318, 4504, 4692

Offset: 0

Author

Jonathan Vos Post, Sep 06 2005

Keywords

• easy
• nonn

Comments

First differences are the sequence of 3-almost primes (A014612). Hence a(n) is the least positive sequence whose first differences are the sequence of 3-almost primes. Primes in this sequence include: a(1) = a(4) = 59, a(17) = 719, a(21) = 1063, a(27) = 1709, a(35) = 2791, a(37) = 3109, . Semiprimes in this sequence include: a(1) = 3^2, a(2) = 21 = 3 * 7, a(3) = 39 = 3 * 13, a(5) = 86 = 2 * 43, a(12) = 377 = 13 * 29, a(20) = 965 = 5 * 193, a(24) = 1369 = 37^2, a(34) = 2638 = 2 * 1319, a(38) = 3274 = 2 * 1637, a(41) = 3787 = 7 * 541, a(42) = 3961 = 17 * 223, a(47) = 4882 = 2 * 2441. 3-almost primes in this sequence include: a(1) = 2^3, a(6) = 114 = 2 * 3 * 19, a(8) = 186 = 2 * 3 * 31, a(9) = 230 = 2 * 5 * 23, a(10) = 275 = 5^2 * 11, a(11) = 325 = 5^2 * 13, a(14) = 506 = 2 * 11 * 23, a(15) = 574 = 2 * 7 * 41, a(18) = 795 = 3 * 5 * 53, a(19) = 873 + 3^2 * 97, a(22) = 1162 = 2 * 7 * 83, a(25) = 1479 = 3 * 17 * 29, a(28) = 1826 = 2 * 11 * 83, a(30) = 2075 = 5^2 * 83, a(32) = 2343 = 3 * 11 * 71, a(36) = 2945 = 5 * 19 * 31, a(40) = 3615 = 3 * 5 * 241, a(44) = 4318 = 2 * 17 * 127. Note also the powers a(7) = 144 = 12^2.

Crossrefs

Cf. A014612, A086062, A110208, A110226.

Formula

a(0) = 1; for n>0, a(n) = 1 + A086062(n).