OFFSET
1,1
COMMENTS
Up to n=10^7 no solution for p+sopfr(n) | n+sopfr(n) and p+sopfr(n) | n-sopfr(n) while p-sopfr(n) | n-sopfr(n) is satisfied by 8216395 and 8880415.
Subsequence of A120944.
EXAMPLE
Prime factors of 37411 are 11, 19 and 179 while sopfr(37411) = 209. We have that 37411 + 209 = 37620 and 37620 / (11 - 209) = -190, 37620 / (19 - 209) = -198 and 37620 / (179 - 209) = -1254.
MAPLE
with (numtheory); P:=proc(q) local a, b, i, ok, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
b:=add(a[i][1]*a[i][2], i=1..nops(a));
for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=b then ok:=0; break;
else if not type((n+b)/(a[i][1]-b), integer) then ok:=0; break; fi; fi; od;
if ok=1 then print(n); fi; fi; od; end: P(10^6);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Aug 20 2013
EXTENSIONS
First term deleted by Paolo P. Lava, Sep 23 2013
a(16)-a(29) from Donovan Johnson, Nov 14 2013
STATUS
approved