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A037992 Smallest number with 2^n divisors. 16
1, 2, 6, 24, 120, 840, 7560, 83160, 1081080, 17297280, 294053760, 5587021440, 128501493120, 3212537328000, 93163582512000, 2888071057872000, 106858629141264000, 4381203794791824000, 188391763176048432000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(500500) mod 500500507 is the solution to Problem 500 on Project Euler. - Danny Rorabaugh, Sep 25 2015

Positions where the number of infinitary divisors of n (A037445), increases to a record (cf. A002182), or infinitary analog of highly composite numbers (A002182). - Vladimir Shevelev, May 13, 22 2016

LINKS

T. D. Noe and Danny Rorabaugh, Table of n, a(n) for n=0..350 (first 101 terms from T. D. Noe)

Project Euler, Problem 500!!!

FORMULA

A000005(a(n)) = A000079(n).

a(n) = prod(k=1, n, A050376(k)), product of the first n entries of A050376(n). - Lekraj Beedassy, Jun 30 2004

a(n) = A052330(2^n -1). - Thomas Ordowski, Jun 29 2005

A001221(a(n+1)) <= A001221(a(n))+1, see also A074239; A007947(a(n)) gives a sequence of primorials (A002110) in nondecreasing order. - Reinhard Zumkeller, Apr 16 2006, corrected: Apr 09 2015

a(n) = A005179(2^n). - Ivan N. Ianakiev, Apr 01 2015

MATHEMATICA

a[0] = 1; a[n_] := a[n] = Catch[ For[ k = 2, True, k++, If[ an = k*a[n-1]; DivisorSigma[0, an] == 2^n, Throw[an]]]]; Table[a[n], {n, 0, 18}] (* Jean-Fran├žois Alcover, Apr 16 2012 *)

PROG

(PARI) {a(n)= local(A, m, c, k, p); if(n<1, n==0, c=0; A=1; m=1; while( c<n, m++; if( isprime(m)| ( (k=ispower(m, (null), &p))&isprime(p)& k ==2^valuation(k, 2) ), A*=m; c++)); A)} /* Michael Somos, Apr 15 2005 */

(Haskell)

a037992 n = head [x | x <- [1..], a000005 x == 2 ^ n]

-- Reinhard Zumkeller, Apr 08 2015

CROSSREFS

Cf. A000005, A000079, A001221, A005179, A007947, A050376, A052330, A074239.

Sequence in context: A292749 A079854 A024923 * A114779 A230363 A275753

Adjacent sequences:  A037989 A037990 A037991 * A037993 A037994 A037995

KEYWORD

nonn,nice,changed

AUTHOR

J. Lowell

EXTENSIONS

a(18) from Don Reble, Aug 20 2002

STATUS

approved

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Last modified October 22 02:43 EDT 2017. Contains 293756 sequences.