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A059591 Squarefree part of n^2+1. 5
1, 2, 5, 10, 17, 26, 37, 2, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 13, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 41, 1090, 1157, 1226, 1297, 1370, 5, 1522, 1601, 2, 1765, 74, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Related to period-1 continued fractions [z,z,z,...].

LINKS

Enrique PĂ©rez Herrero, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = A007913(n^2+1).

a(n)*A059592(n)^2 = n^2+1.

EXAMPLE

a(7)=2 since 7^2+1 = 50 = 25*2 = (5^2)*2.

MAPLE

A:= proc(n)

local F;

F:= select(t -> t[2]::odd, ifactors(n^2+1)[2]);

mul(t[1], t=F)

end proc:

map(A, [$0..100]); # Robert Israel, Jun 18 2015

MATHEMATICA

Table[Times @@ Flatten[Table[#1, {#2}] & @@@ Select[FactorInteger[n^2 + 1], OddQ@ Last@ # &]], {n, 120}] (* Michael De Vlieger, Jun 19 2015 *)

PROG

(PARI) a(n) = core(n^2+1); \\ Michel Marcus, Jun 18 2015

CROSSREFS

Cf. A007913, A059592, A000188.

Sequence in context: A078393 A100292 A078325 * A082607 A159547 A002522

Adjacent sequences:  A059588 A059589 A059590 * A059592 A059593 A059594

KEYWORD

easy,nonn

AUTHOR

Marc LeBrun, Jan 25 2001

STATUS

approved

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Last modified May 26 05:18 EDT 2017. Contains 287074 sequences.