

A287923


Numbers equal to the sum of the prime factors, with multiplicity, of the previous and of the following k numbers, for some k.


1



260, 3100, 4699, 29318, 54760, 82952, 315657, 380741, 574883, 873815, 949282, 1766959, 2114033, 3971361, 5418111, 6972931, 7644772, 9714402, 15752927, 30118112, 91750525, 129381240, 130672476, 395713882, 450192670, 523370293, 553444691, 833889991
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Similar to A257367 but here the prime factors of a(n) are not considered.
Again, while in A257367 the prime numbers are not allowed because they would be just a trivial solution, here they are part of the terms of the sequence. The first one is 15752927.
Values of k are 2, 2, 3, 6, 4, 7, 5, 4, 7, 8, 11, 11, 5, 8, 11, 11, 9, 5, 9, 15, 14, 7, 9, 10, 12, 17, 19, 33, ...
Numbers tested up to 10^9.


LINKS



FORMULA



EXAMPLE

258 = 2*3*43, 259 = 7*37, 261 = 3*3*29, 262 = 2*131 and 2 + 3 + 43 + 7 + 37 + 3 + 3 + 29 + 2 + 131 = 260.


MAPLE

with(numtheory): P:= proc(q) local a, b, c, k, n;
for n from 1 to q do a:=0; k:=0; while a<n do k:=k+1;
b:=ifactors(nk)[2]; b:=add(b[j][1]*b[j][2], j=1..nops(b));
c:=ifactors(n+k)[2]; c:=add(c[j][1]*c[j][2], j=1..nops(c));
a:=a+b+c; od; if a=n then print(n); fi; od; end: P(10^9);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



