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A219017
Smallest number k such that k^2 - 1 has exactly n distinct prime factors.
4
2, 4, 11, 29, 131, 419, 1429, 14629, 77141, 509081, 1456729, 22486309, 117048931, 1625292241, 10326137821, 117440297701, 1110819807371, 8678298841211, 138645880242871, 980010587880169
OFFSET
1,1
COMMENTS
a(14) <= 1625292241. - Donovan Johnson, Nov 10 2012
LINKS
EXAMPLE
a(3) = 11 is the smallest number of the set {k(i)} = {11, 13, 14, 16, 19, 20, ...} where k(i)^2 - 1 contains 3 distinct prime factors.
a(10) = 509081 because 509081^2-1 = 2 ^ 4 * 3 * 5 * 7 * 11 * 13 * 17 * 23 * 31 * 89 with 10 distinct prime factors.
MAPLE
with(numtheory) :for n from 1 to 11 do:ii:=0:for k from 1 to 10^10 while(ii=0) do:x:=k^2-1:y:=factorset(x):n1:=nops(y):if n1=n then ii:=1: printf ( "%d %d \n", n, k):
else fi:od:od:
MATHEMATICA
L = {}; Do[n = 2; While[Length[FactorInteger[n^2 - 1]] != k, n++]; Print@AppendTo[L, n], {k, 15}] (* Giovanni Resta, Nov 10 2012 *)
CROSSREFS
Cf. A180278.
Sequence in context: A148148 A148149 A034769 * A285216 A212422 A189832
KEYWORD
nonn,hard,more
AUTHOR
Michel Lagneau, Nov 09 2012
EXTENSIONS
a(12)-a(13) from Donovan Johnson, Nov 10 2012
a(14)-a(17) from Giovanni Resta, May 10 2017
a(18) from Michael S. Branicky, Feb 08 2023
a(19) from Michael S. Branicky, Feb 15 2023
a(20) from Michael S. Branicky, Feb 19 2023
Name clarified by Pontus von Brömssen, Sep 12 2023
STATUS
approved