A257929 Primes equal to the sum of the prime factors, with multiplicity, of the next k numbers, for some k.

5, 19, 37, 139, 262880929, 1551042113, 64548518479, 1573353619909

Offset

1,1

Comments

Values of k are 1, 2, 2, 3, 17, 10, 25, 51, ...

a(9) > 3*10^12. - Giovanni Resta, May 16 2015

Links

Table of n, a(n) for n=1..8.

Example

For 5, consider the prime factors of the next number, 6: 2, 3. Their sum is 2 + 3 = 5.
For 19, consider the prime factors of the next 2 numbers, 20, 21: 2, 2, 5; 3, 7. Their sum is 2 + 2 + 5 + 3 + 7 = 19.

Maple

with(numtheory): P:= proc(q) local a, d, j, k, n;
for n from 2 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);

Prog

(PARI) sopfr(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]);
isok(n) = {my(s = 0); my(k = 1); while (s < n, s += sopfr(n+k); k++); s == n; }
lista(nn) = {forprime(n=2, nn, if (isok(n), print1(n, ", ")); ); } \\ Michel Marcus, May 27 2015

Crossrefs

Cf. A257524, A257525.

Sequence in context: A285226 A146861 A068963 * A254060 A129828 A239831

Adjacent sequences: A257926 A257927 A257928 * A257930 A257931 A257932

Keyword

nonn,more

Author

Paolo P. Lava, May 13 2015

Extensions

a(6)-a(8) from Giovanni Resta, May 16 2015

Status

approved