A075721 a(n+1) = least k with sum of prime factors (with repetition) = a(n)+1 with a(0) = 2.

2, 3, 4, 5, 8, 14, 26, 92, 356, 1412, 5636, 185559, 556671, 21152738, 42305474, 2919075981, 14595379885, 102167659153, 3882371047054, 361060507372953, 16969843846526629, 1561225633880447476, 6244902535521789892

Offset

0,1

Links

Table of n, a(n) for n=0..22.

Jason Earls, A note on the Smarandache divisors of divisors sequence and two similar sequences, in Smarandache Notions Journal (2004), Vol. 14.1, page 275. [broken link]

Example

92 is a term because it is the smallest number whose sum of prime factors is equal to the previous term + 1; 92 = 2^2*23 and 2+2+23 = 26+1.

Mathematica

Nest[Append[#, Block[{k = #[[-1]] + 1, m}, m = k; While[Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger@ k] != m, k++]; k]] &, {2}, 12] (* Michael De Vlieger, Mar 28 2018 *)

Prog

(PARI) v = vector(200); count = 0; m = 2; print1("2 3 4 5 8 "); n = 8; while (count < 199, f = factor(m); s = sum(i = 1, matsize(f)[1], f[i, 1]*f[i, 2]); if (s <= 200 && v[s] == 0, count++; v[s] = m); m++); for (i = 1, 20, p = precprime(n + 1); if (p == n + 1, n++; print1(n, " "), b = v[n + 1 - p]; c = p; while (b > n + 1 - p, p = precprime(p - 1); m = v[n + 1 - p]; if (m < b, b = m; c = p)); n = b*c; print1(n, " "))); \\ David Wasserman, Jan 23 2005

Crossrefs

Sequence in context: A015925 A140294 A108014 * A112479 A333264 A247461

Adjacent sequences: A075718 A075719 A075720 * A075722 A075723 A075724

Keyword

nonn

Author

Jason Earls, Oct 03 2002

Extensions

More terms from David Wasserman, Jan 23 2005

Status

approved