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 A119361 a(n) is the n-th positive integer which is divisible by the same distinct primes as n and which is divisible by no other primes. 1
 1, 4, 27, 16, 3125, 48, 823543, 256, 19683, 320, 285311670611, 162, 302875106592253, 1568, 5625, 65536, 827240261886336764177, 432, 1978419655660313589123979, 2500, 50421, 22528, 20880467999847912034355032910567, 972, 298023223876953125, 70304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that a(n) is rad(n) times the n-th smallest divisor of n^n, i.e., A007947(n)*A121067(n). [Hagen von Eitzen, Jul 20 2009; Charles R Greathouse IV, Oct 09 2016] LINKS Hagen von Eitzen and Robert Israel, Table of n, a(n) for n = 1..388 (n = 1..50 from Hagen von Eitzen) EXAMPLE 6 = 2*3. The sequence of positive integers which are divisible by 2 and 3, but not divisible by any other primes, is 6,12,18,24,36,48,54,... The 6th such integer is 48, so a(6) = 48. MAPLE f:= proc(n) local P, r, Cands, j, B; P:= sort(convert(numtheory:-factorset(n), list)); r:= convert(P, `*`); Cands:= [seq(r*P[1]^i, i=0..n-1)]; for j from 2 to nops(P) do B:= Cands[n]; Cands:= sort(map(c -> seq(c*P[j]^i, i=0..floor(log[P[j]](B/c))), Cands)); Cands:= Cands[1..n]; od; Cands[n] end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Oct 09 2016 MATHEMATICA f[n_] := Module[{P, r, Cands, j, B}, P = FactorInteger[n][[All, 1]]; r = Times @@ P; Cands = Table[r P[[1]]^i, {i, 0, n-1}]; Do[B = Cands[[n]]; Cands = Table[# P[[j]]^i, {i, 0, Floor[Log[P[[j]], B/#]]}]& /@ Cands // Flatten // Sort; Cands = Cands[[1;; n]], {j, 2, Length[P]}]; Cands[[n]]]; f[1] = 1; f /@ Range[100] (* Jean-François Alcover, Sep 17 2020, after Robert Israel *) CROSSREFS Sequence in context: A136511 A218362 A108138 * A133482 A108139 A351365 Adjacent sequences: A119358 A119359 A119360 * A119362 A119363 A119364 KEYWORD nonn AUTHOR Leroy Quet, Jul 24 2006 EXTENSIONS More terms from Joshua Zucker, Aug 12 2006 More terms copied from b-file by Hagen von Eitzen, Jul 20 2009 STATUS approved

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Last modified August 8 18:48 EDT 2024. Contains 375023 sequences. (Running on oeis4.)