A216895 n - (sum of prime factors of n^2+1) is prime.

57, 117, 174, 192, 193, 212, 268, 336, 342, 360, 394, 408, 448, 498, 560, 606, 746, 748, 818, 822, 882, 924, 931, 1052, 1087, 1196, 1227, 1254, 1280, 1380, 1390, 1404, 1432, 1477, 1478, 1514, 1534, 1590, 1633, 1696, 1702, 1818, 1856, 1874, 1903, 2057, 2108

Offset

1,1

Comments

Prime factors counted without multiplicity. - Harvey P. Dale, Jul 04 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

57 is in the sequence because the prime divisors of  57^2 + 1 = 3250 are {2, 5, 13}, and 57 - (2+5+13) = 37 is prime.

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):if n> s and type(n-s, prime)=true then printf(`%d, `, n): else fi:od:

Mathematica

spfpQ[n_]:=Module[{c=Total[FactorInteger[n^2+1][[All, 1]]]}, n>c && PrimeQ[ n-c]]; Select[Range[2500], spfpQ] (* Harvey P. Dale, Jul 04 2017 *)

Crossrefs

Cf. A008472.

Sequence in context: A039535 A037990 A296298 * A044244 A044625 A304841

Adjacent sequences: A216892 A216893 A216894 * A216896 A216897 A216898

Keyword

nonn

Author

Michel Lagneau, Sep 19 2012

Status

approved