A169802 Numbers k equal to A074036(k) = sum of primes from least to largest prime factor.

2, 3, 5, 7, 10, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 155, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Author

N. J. A. Sloane, May 24 2010

Keywords

• nonn

Comments

Union of primes (A000040) and A055233.

Links

• Erich Friedman, What's Special About This Number?

Crossrefs

Cf. A055233 (this without primes), A074036 (sum of primes from spf(n) to gpf(n)).

Cf. A020639 (spf: smallest prime factor), A006530 (gpf: greatest prime factor).

Programs

Mathematica

upto=500;a={};Do[f=Map[First,FactorInteger[k]];If[k==Total[Select[Range[First[f],Last[f]],PrimeQ]],AppendTo[a,k]],{k,upto}]; a (* Paolo Xausa, Nov 27 2021 *)

PARI

select( {is_A169802(n,f=factor(n)[,1])=n>1&&n==vecsum(primes([f[1],f[#f]]))}, [1..222]) \\ M. F. Hasler, Nov 24 2021