A257976 - OEIS

%I #34 Mar 02 2019 01:54:46

%S 23,94,123,147,269,806,1049,1081,1179,1277,1775,2575,5374,14865,20490,

%T 20845,27177,54934,72599,87031,101827,391514,452574,534389,1197146,

%U 1219229,1297767,1327510,4565354,4946164,6124646,7967984,8637602,8869951,9615708,10061718

%N Numbers equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k.

%C Number of terms < 10^k: 0, 2, 6, 13, 20, 24, 35, 49, 62, 68, 79, 91, ..., . - _Robert G. Wilson v_, May 19 2015

%H Giovanni Resta, <a href="/A257976/b257976.txt">Table of n, a(n) for n = 1..91</a> (terms < 10^12, first 58 terms from Robert G. Wilson v)

%t sopfr[n_] := Plus @@ Times @@@ FactorInteger@ n; sopfr[1] = 0; ls = Table[0, {50}]; k = 1; lst = {}; While[k < 10^7, If[ MemberQ[ Accumulate@ ls, k], AppendTo[lst, k]]; ls = Join[{sopfr@ k}, Drop[ls, -1]]; k++]; lst (* dated May 15 2015 and modified after a suggestion from Giovanni Resta in a private e-mail dated Apr 20 2015 to _Robert G. Wilson v_, May 21 2015 *)

%o (PARI) sopfr(n)=my(f=factor(n));sum(i=1,#f[,1],f[i,1]*f[i,2]);

%o is(n)=if(n<23,return(0)); my(s); for(k=1,n, s+=sopfr(n-k); if(s>=n, return(n==s))) \\ _Charles R Greathouse IV_, May 15 2015

%Y Union of A257525 and A257930 which are disjoint.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, May 15 2015