A257976 Numbers equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k.

23, 94, 123, 147, 269, 806, 1049, 1081, 1179, 1277, 1775, 2575, 5374, 14865, 20490, 20845, 27177, 54934, 72599, 87031, 101827, 391514, 452574, 534389, 1197146, 1219229, 1297767, 1327510, 4565354, 4946164, 6124646, 7967984, 8637602, 8869951, 9615708, 10061718

Offset

1,1

Comments

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..91 (terms < 10^12, first 58 terms from Robert G. Wilson v)

Mathematica

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 *)

Prog

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

Crossrefs

Union of A257525 and A257930 which are disjoint.

Sequence in context: A244632 A042030 A042032 * A183011 A158544 A154376

Adjacent sequences: A257973 A257974 A257975 * A257977 A257978 A257979

Keyword

nonn

Author

Robert G. Wilson v, May 15 2015

Status

approved