A257929 - OEIS

%I #21 May 28 2015 03:45:40

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

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

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

%C a(9) > 3*10^12. - _Giovanni Resta_, May 16 2015

%e For 5, consider the prime factors of the next number, 6: 2, 3. Their sum is 2 + 3 = 5.

%e 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.

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

%p for n from 2 to q do if 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) = {forprime(n=2, nn, if (isok(n), print1(n, ", ")););} \\ _Michel Marcus_, May 27 2015

%Y Cf. A257524, A257525.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, May 13 2015

%E a(6)-a(8) from _Giovanni Resta_, May 16 2015