A216896 n - (sum of prime factors of n^2+1) is a positive square.

38, 133, 172, 253, 460, 477, 580, 612, 717, 996, 1057, 1568, 1641, 2244, 2820, 3193, 3253, 3652, 3848, 4284, 4733, 4900, 4908, 5063, 5380, 6396, 7220, 8712, 9245, 9972, 10061, 10181, 10723, 11316, 11492, 12488, 12549, 12567, 13439, 14063, 14597, 15660, 15683

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

38 is in the sequence because the prime divisors of 38^2 + 1 = 1445 are {5, 17}, and 38 - (5+17) = 16 is square.

Maple

with(numtheory): for n from 1 to 2500 do:x:=n^2+1:y:=factorset(x):n1:=nops(y): s:=sum('y[i] ', 'i'=1..n1):z:=n-s:if n> s and sqrt(z)=floor(sqrt(z)) then printf(`%d, `, n): else fi:od:

Mathematica

aQ[n_] := (s = n - Plus @@ First @ Transpose @ FactorInteger[n^2+1]) > 0 && IntegerQ @ Sqrt @ s; Select[Range[16000], aQ] (* Amiram Eldar, Sep 09 2019 *)

Crossrefs

Cf. A193462.

Sequence in context: A044289 A044670 A118633 * A158525 A044370 A044751

Adjacent sequences: A216893 A216894 A216895 * A216897 A216898 A216899

Keyword

nonn

Author

Michel Lagneau, Sep 19 2012

Status

approved