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A257525 Composite numbers equal to the sum of the prime factors, with multiplicity, of the previous k numbers, for some k. 6

%I

%S 94,123,147,806,1081,1179,1775,2575,5374,14865,20490,20845,27177,

%T 54934,72599,87031,101827,391514,452574,534389,1197146,1219229,

%U 1297767,1327510,4565354,4946164,6124646,7967984,8637602,9615708,10061718,14563178,18997520,24277270

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

%C 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, ...

%H Paolo P. Lava, <a href="/A257525/a257525.txt">First 50 terms with associated k values</a>

%e 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.

%e For 123, condider 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.

%p with(numtheory): P:= proc(q) local a,d,j,k,n;

%p for n from 2 to q do if not isprime(n) then a:=0; k:=0;

%p while a<n do k:=k+1; d:=ifactors(n-k)[2];

%p d:=add(d[j][1]*d[j][2],j=1..nops(d));

%p a:=a+d; od; if a=n then print(n);

%p fi; fi; od; end: P(10^9);

%o (PARI) sopfr(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]);

%o isok(n) = {my(s = 0); my(k = 1); while (s < n, s += sopfr(n-k); k++); s == n;}

%o lista(nn) = {forcomposite(n=2, nn, if (isok(n), print1(n, ", ")););} \\ _Michel Marcus_, May 27 2015

%Y Cf. A257367, A257524, A257929, A257930.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Apr 28 2015

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Last modified November 18 02:05 EST 2019. Contains 329242 sequences. (Running on oeis4.)