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A267422 Largest prime factor of the largest squarefree practical number comprising n prime factors. 0
2, 3, 13, 167, 28219, 796481281, 634382430983400959, 402441068740409482305343048128921493, 161958813808922990180784918278423278413890512706478208244331277280870341 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that the prime factors of the largest squarefree practical number with n prime factors are the first n members of a(n). The largest squarefree practical number with 3 prime factors is 78 = 2*3*13 and the largest squarefree practical number with 5 prime factors is 367580694 = 2*3*13*167*28219, etc.

LINKS

Table of n, a(n) for n=1..9.

Wikipedia, Practical number and Squarefree integer

EXAMPLE

a(3) = 13 because there are only 4 squarefree practical numbers with 3 prime factors, namely 2*3*5 = 30, 2*3*7 = 42, 2*3*11 = 66 and 2*3*13 = 78. So 78 is the largest squarefree practical number with 3 prime factors and the largest prime factor is 13.

MATHEMATICA

lst={2}; Do[If[PrimeQ[f=DivisorSigma[1, Apply[Times, lst]]+1], AppendTo[lst, f], AppendTo[lst, NextPrime[f, -1]]], {8}]; lst

CROSSREFS

Cf. A005117, A005153, A265501.

Sequence in context: A153888 A068083 A137459 * A072162 A113785 A118323

Adjacent sequences:  A267419 A267420 A267421 * A267423 A267424 A267425

KEYWORD

nonn,more

AUTHOR

Frank M Jackson, Jan 14 2016

STATUS

approved

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)