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A070600 Largest number with n prime factors where all factors are less than or equal to n. 0
0, 4, 27, 81, 3125, 15625, 823543, 5764801, 40353607, 282475249, 285311670611, 3138428376721, 302875106592253, 3937376385699289, 51185893014090757, 665416609183179841, 827240261886336764177, 14063084452067724991009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = A007917(n)^n for n>1. - Michel Marcus, Sep 24 2020

EXAMPLE

a(2) = 4 (4=2*2 has 2 factors and 2 is the largest prime number <= 2).

a(3) = 27 (27=3*3*3 has 3 factors and 3 is the largest prime number <= 3).

a(4) = 81 (81=3*3*3*3 has 4 factors and 3 is the largest prime number <= 4).

MATHEMATICA

a[n_] := If[n == 1, 0, If[PrimeQ[n], n, NextPrime[n, -1]]^n];

Array[a, 18] (* Jean-Fran├žois Alcover, Sep 24 2020 *)

PROG

(PARI) a(n) = if (n==1, 0, precprime(n)^n); \\ Michel Marcus, Sep 24 2020

CROSSREFS

Cf. A007917 (largest prime <= n).

Sequence in context: A266011 A015238 A298987 * A100488 A220019 A225902

Adjacent sequences:  A070597 A070598 A070599 * A070601 A070602 A070603

KEYWORD

easy,nonn

AUTHOR

Jostein Trondal (jallamekk(AT)hotmail.com), May 13 2002

STATUS

approved

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)