A257930 Primes equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k.

23, 269, 1049, 1277, 8869951, 972928919, 74885169679

Offset

1,1

Comments

Values of k are 2, 5, 4, 12, 12, 19, 37, ...

a(8) > 10^12. - Giovanni Resta, May 15 2015

Subsequence of prime terms of A257976. - Robert G. Wilson v, May 19 2015

Links

Table of n, a(n) for n=1..7.

Example

For 23, consider the prime factors of the previous 2 numbers, 21, 22: 3, 7; 2, 11. Their sum is 3 + 7 + 2 + 11 = 23.
For 269, consider the prime factors of the previous 5 numbers, 264, 265, 266, 267, 268: 2, 2, 2, 3, 11; 5, 53; 2, 7, 19; 3, 89; 2, 2, 67. Their sum is 2 + 2 + 2 + 3 + 11 + 5 + 53 + 2 + 7 + 19 + 3 + 89 + 2 + 2 + 67 = 269.

Maple

with(numtheory): P:= proc(q) local a, d, j, k, n;
for n from 3 to q do if isprime(n) then a:=0; k:=0;
while a<n do k:=k+1; d:=ifactors(n-k)[2];
d:=add(d[j][1]*d[j][2], j=1..nops(d));
a:=a+d; od; if a=n then print(n);
fi; fi; od; end: P(10^9);

Mathematica

sopfr[n_] := Plus @@ Times @@@ FactorInteger@ n; fQ[n_] := Block[{k = n - 1, s = 0}, While[s += sopfr@ k; s < n, k--]; s == n]; p = 5; lst = {}; While[p < 100000000, If[ fQ@ p, AppendTo[lst, p]]; p = NextPrime@ p]; lst (* Robert G. Wilson v, May 15 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 && isprime(n)))) \\ Charles R Greathouse IV, May 15 2015

Crossrefs

Cf. A257367, A257524.

Sequence in context: A002681 A240876 A142220 * A142027 A161523 A161930

Adjacent sequences: A257927 A257928 A257929 * A257931 A257932 A257933

Keyword

nonn,more

Author

Paolo P. Lava, May 13 2015

Extensions

a(6)-a(7) from Giovanni Resta, May 15 2015

Status

approved