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A216896 n - (sum of prime factors of n^2+1) is a positive square. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 07:09 EDT 2021. Contains 345374 sequences. (Running on oeis4.)