A257525 Composite numbers equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k.

94, 123, 147, 806, 1081, 1179, 1775, 2575, 5374, 14865, 20490, 20845, 27177, 54934, 72599, 87031, 101827, 391514, 452574, 534389, 1197146, 1219229, 1297767, 1327510, 4565354, 4946164, 6124646, 7967984, 8637602, 9615708, 10061718, 14563178, 18997520, 24277270

Offset

1,1

Comments

Values of k are 4, 4, 4, 8, 8, 7, 7, 8, 9, 13, 5, 19, 14, 14, 5, 17, 11, 21, 17, 5, 12, 10, 22, 14, 23, 24, 19, 17, 18, 22, 34, 8, 38, 35, ...

Links

Table of n, a(n) for n=1..34.

Paolo P. Lava, First 50 terms with associated k values

Example

For 94, consider the prime factors of the previous 4 numbers, 90, 91, 92, 93: 2, 3, 3, 5; 7, 13; 2, 2, 23; 3, 31. Their sum is 2 + 3 + 3 + 5 + 7 + 13 + 2 + 2 + 23 + 3 + 31 = 94.
For 123, consider the prime factors of the previous 4 numbers, 119, 120, 121, 122: 7, 17; 2, 2, 2, 3, 5; 11, 11; 2, 61. Their sum is 7 + 17 + 2 + 2 + 2 + 3 + 5 + 11 + 11 + 2 + 61 = 123.

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, A257524, A257929, A257930.

Sequence in context: A146336 A269988 A044974 * A020355 A039551 A100767

Adjacent sequences: A257522 A257523 A257524 * A257526 A257527 A257528

Keyword

nonn

Author

Paolo P. Lava, Apr 28 2015

Status

approved