The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A293570 a(-1)=4; thereafter a(n) is the least integer m such that the product of the divisors of m is m^n. 2
 4, 1, 2, 6, 12, 24, 48, 60, 192, 120, 180, 240, 3072, 360, 12288, 960, 720, 840, 196608, 1260, 786432, 1680, 2880, 15360, 12582912, 2520, 6480, 61440, 6300, 6720, 805306368, 5040, 3221225472, 7560, 46080, 983040, 25920, 10080, 206158430208, 3932160, 184320, 15120, 3298534883328, 20160, 13194139533312, 107520, 25200, 62914560 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,1 COMMENTS First occurrence of k in A292286. Records occur for 4, 6, 12, 24, 48, 60, 192, 240, 3072, 12288, 196608, 786432, 12582912, 805306368, 3221225472, etc. Terms not a multiple of 60: 1, 2, 4, 6, 12, 24, 48, 192, 3072, 12288, 196608, 786432, 12582912, 805306368, 3221225472, etc. From Robert Israel, Nov 01 2017: (Start) All terms are in A025487. For n >= 1, if a(n) = Product_{i=1..k} prime(i)^e(i) then n = (1/2)*Product_{i=1..k} (e(i)+1). If p is prime, a(p) = 2^(p-1)*3. (End) LINKS Robert Israel, Table of n, a(n) for n = -1..3318 FORMULA a(n) = A003680(n), for n > 0. - Paolo P. Lava, May 04 2018 MAPLE g:= proc(F, k) # minimize Product_{i>=k} prime(i)^(e(i)-1) s.t. Product_{i>=k} e(i) = n # return [v, E] where E the list of e(i) and v the value # F the prime factorization of n   uses combinat;   local e, pk, Fv, gv, v, vmin, gmin, T, t, gpf;   if F = [] then return [1, []] fi;   vmin:= infinity;   gpf:= F[-1][1];   pk:= ithprime(k);   T:= cartprod([seq([\$0..f[2]], f = F)]);   while not T[finished] do     t:= T[nextvalue]();     e:= mul(F[i][1]^t[i], i=1..nops(F));     if e < gpf then next fi;     Fv:= [seq(`if`(t[i] = F[i][2], NULL, [F[i][1], F[i][2]-t[i]]), i=1..nops(F))];     gv:= procname(Fv, k+1);     v:= pk^(e-1) * gv[1];     if v < vmin then        vmin:= v;        gmin:= [e, op(gv[2])];     fi   od;   [vmin, gmin] end proc: 4, seq(g(ifactors(2*n)[2], 1)[1], n=0..50); # Robert Israel, Nov 01 2017 MATHEMATICA f[n_] := Boole[n == 1] + If[OddQ@#, -1, #/2] &@DivisorSigma[0, n]; t[_] = 0; k = 1; While[k < 3300000000, a = f@k; If[ t[a] == 0, t[a] = k; Print[{a, k}]]; k ++]; t@# & /@ Range[-1, 36] PROG (PARI) a(n) = if(n == 0 || n == -1, return((n-1)^2)); for(m=2, +oo, my(p=1); fordiv(m, d, p*=d); if(p == m^n, return(m))) \\ Iain Fox, Dec 14 2017 CROSSREFS Cf. A003680, A007955, A025487, A292286. Sequence in context: A343404 A220182 A076064 * A016685 A141332 A241184 Adjacent sequences:  A293567 A293568 A293569 * A293571 A293572 A293573 KEYWORD nonn AUTHOR Robert G. Wilson v, Oct 12 2017 EXTENSIONS More terms from Robert Israel, Nov 01 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 1 11:07 EDT 2021. Contains 346385 sequences. (Running on oeis4.)