A347064 -id:A347064 - cp's OEIS frontend

A352870 Ratios of consecutive terms of A347064, or 0 if ratio is not an integer.

2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 71, 73, 78, 79, 83, 89, 97, 101, 103, 107, 109, 113, 119, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 0, 191, 193, 197, 199, 211, 216, 223, 227, 229

Offset: 1

J. Lowell, Apr 06 2022

nonn

a(51)=0; quotient is the non-integer 2185/12.

			A347064(18) is 42 times A347064(17) so a(18) = 42.

Cf. A347064.

a(n) = A347064(n)/A347064(n-1) if integer, otherwise 0.

A037992 Smallest number with 2^n divisors.

Original entry on oeis.org

1, 2, 6, 24, 120, 840, 7560, 83160, 1081080, 17297280, 294053760, 5587021440, 128501493120, 3212537328000, 93163582512000, 2888071057872000, 106858629141264000, 4381203794791824000, 188391763176048432000, 8854412869274276304000, 433866230594439538896000

Offset: 0

J. Lowell

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

Danny Rorabaugh, Table of n, a(n) for n = 0..350 (first 101 terms from T. D. Noe)
Project Euler, Problem 500!!!

Cf. A000005, A000079, A001221, A005179, A007947, A050376, A052330, A074239, A347064.

a037992 n = head [x | x <- [1..], a000005 x == 2 ^ n]
-- Reinhard Zumkeller, Apr 08 2015

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 *)

{a(n)= local(A,m,c,k,p); if(n<1, n==0, c=0; A=1; m=1; while( cMichael Somos, Apr 15 2005 */

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

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

a(18) from Don Reble, Aug 20 2002

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A352870 Ratios of consecutive terms of A347064, or 0 if ratio is not an integer.

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A037992 Smallest number with 2^n divisors.

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