A257524 Composite numbers equal to the sum of the prime factors, with multiplicity, of the next k numbers, for some k.

49, 132, 1070, 1140, 2862, 40652, 158170, 204252, 365859, 656092, 806526, 812571, 861444, 1031941, 4017612, 4227164, 8045675, 15843252, 16298931, 48625784, 81869208, 129071545, 142516026, 219039320, 266299218, 520700301, 537506243, 590578292, 600500937, 915352703

Offset

1,1

Comments

Values of k are 3, 4, 8, 5, 9, 9, 17, 25, 22, 18, 11, 15, 9, 20, 10, 12, 21, 26, 30, 25, 15, 14, 21, 30, 22, 26, 20, 13, 19, 11, ...

Links

Table of n, a(n) for n=1..30.

Example

For 49, consider the prime factors of the next 3 numbers, 50, 51, 52: 2, 5, 5; 3, 17; 2, 2, 13. Their sum is 2 + 5 + 5 + 3 + 17 + 2 + 2 + 13 = 49.
For 132, consider the prime factors of the next 4 numbers, 133, 134, 135, 136: 7, 19; 2, 67; 3, 3, 3, 5; 2, 2, 2, 17. Their sum is 7 + 19 + 2 + 67 + 3 + 3 + 3 + 5 + 2 + 2 + 2 + 17 = 132.

Maple

with(numtheory): P:= proc(q) local a, d, j, k, n;
for n from 2 to q do if not 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) = {forcomposite(n=2, nn, if (isok(n), print1(n, ", ")); ); } \\ Michel Marcus, May 27 2015

Crossrefs

Cf. A257367, A257525, A257929, A257930.

Sequence in context: A250311 A211727 A304674 * A020256 A304171 A118160

Adjacent sequences: A257521 A257522 A257523 * A257525 A257526 A257527

Keyword

nonn

Author

Paolo P. Lava, Apr 28 2015

Status

approved