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A180278 a(n) = k is the smallest number such that k^2 + 1 contains n distinct prime factors. 10
0, 1, 3, 13, 47, 447, 2163, 24263, 241727, 2923783, 16485763, 169053487, 4535472963 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(12) <= 5755933903. - Donovan Johnson, Aug 27 2012

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) >= sqrt(A185952(n)-1). - Charles R Greathouse IV, Feb 17 2015

EXAMPLE

a(2) = 3 because the 2 distinct prime factors of 3^2 + 1 are {2, 5} ;

a(10) = 16485763 because the 10 distinct prime factors of 16485763^2 + 1 are {2, 5, 13, 17, 29, 37, 41, 73, 149, 257}.

MATHEMATICA

k = 1; Table[While[Length[FactorInteger[1 + k^2]] != n, k++]; k, {n, 5}]

PROG

(PARI) print1(r=0); for(n=1, 1e9, t=omega(n^2+1); if(t>r, r++; print1(", "n); n--)) \\ Charles R Greathouse IV, Feb 17 2015

CROSSREFS

Cf. A002522, A002144, A219017.

Sequence in context: A304628 A265920 A262322 * A193164 A122424 A027326

Adjacent sequences:  A180275 A180276 A180277 * A180279 A180280 A180281

KEYWORD

nonn,hard

AUTHOR

Michel Lagneau, Jan 17 2011

EXTENSIONS

a(9), a(10) and example corrected; a(11) added, Donovan Johnson, Aug 27 2012

a(12) from Giovanni Resta, May 10 2017

STATUS

approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)