login
Numbers k equal to A074036(k) = sum of primes from least to largest prime factor.
3

%I #12 Dec 04 2021 12:39:46

%S 2,3,5,7,10,11,13,17,19,23,29,31,37,39,41,43,47,53,59,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,127,131,137,139,149,151,155,157,163,167,

%U 173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271

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

%C Union of primes (A000040) and A055233.

%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a>

%t 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 *)

%o (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

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

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 24 2010