OFFSET
0,2
COMMENTS
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
Infinitary superabundant numbers: numbers m with record values of the infinitary abundancy index, A049417(m)/m > A049417(k)/k for all k < m. - Amiram Eldar, Sep 20 2019
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..350 (first 101 terms from T. D. Noe)
Project Euler, Problem 500!!!
FORMULA
a(n) = Product_{k=1..n} A050376(k), product of the first n terms of A050376. - 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
a(n+1)/a(n) = A050376(n+1). - Jinyuan Wang, Oct 14 2018
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-François 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, , &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
(Python)
def a(n):
product = 1
k = 1
for i in range(n+1):
product *= k # k=A050376(i), for i>=1
while product % k == 0:
k += 1
return product
# Jason L. Miller, Mar 20 2024
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
a(18) from Don Reble, Aug 20 2002
STATUS
approved