OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..144 (terms below 10^9, terms 1..77 from Lukas Naatz)
EXAMPLE
11293 is in the sequence because 11293^2+1 = 2 * 5 ^ 2 * 29 * 281 * 313 and 313 + 2 = 5 + 29 + 281 = 315.
MAPLE
isA192771 := proc(n) local p, s1, n2 ; n2 := n^2+1 ; if A001221(n2) = 5 then p := numtheory[factorset](n2) ; s1 := max(op(p)) + min( op(p)) ; evalb( add(k, k=p) = 2*s1 ) ; else false; end if; end proc:
for n from 1 do if isA192771(n) then printf("%d, \n", n); end if; end do: # R. J. Mathar, Jul 11 2011
MATHEMATICA
seqQ[n_] := Module[{p = FactorInteger[n^2 + 1][[;; , 1]]}, Length[p] == 5 && p[[1]] + p[[5]] == p[[2]] + p[[3]] + p[[4]]]; Select[Range[10^6], seqQ] (* Amiram Eldar, Jan 15 2020 *)
PROG
(PARI) for(k=1, 5000000, my(f=factor(k^2+1)); if(#f[, 2]==5, if(f[1, 1]+f[5, 1]==f[2, 1]+f[3, 1]+f[4, 1], print1(k, ", ")))) \\ Hugo Pfoertner, Jan 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 09 2011
EXTENSIONS
a(17) and beyond from Lukas Naatz, Jan 08 2020
STATUS
approved