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A257525
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Composite numbers equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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