A241813 Numbers disqualified from being in A019505 for not being the smallest number with their respective number of divisors.

8, 96, 480, 1440, 40320, 443520, 1330560, 34594560, 86486400, 588107520, 1470268800, 11174042880, 55870214400, 195545750400, 1285014931200, 17990209036800, 53970627110400, 1565148186201600, 194078375088998400, 7180899878292940800, 35904499391464704000, 294416895010010572800

Offset: 1

Author

J. Lowell, Apr 29 2014

Keywords

• nonn
• more

Comments

It appears that when 2*A019505(n) is a member of this sequence then the exponent in at least one primary of the factorization of A019505(n+1) is smaller than in the corresponding primary of A019505(n) or A019505(n+1) contains an additional prime factor. The smallest example in this sequence where two primaries have smaller exponents and an additional prime factor is added is a(14) = 2*A019505(43) = 2 * 97772875200 = 195545750400. The sequence of exponents of its primaries is (7, 3, 2, 2, 1, 1, 1, 1 ) while A019505(44) = 160626866400 has exponent sequence (5, 3, 2, 1, 1, 1, 1, 1, 1 ). - Hartmut F. W. Hoft, Feb 22 2023

Examples

			8 qualifies because 8 = 4*2 and 4 is in A019505, but 8 can't be term after 4 in A019505 because smallest number with 4 divisors is 6.
		

Crossrefs

Cf. A019505, A140635.

Programs

Mathematica

dataA019505 = Map[Last, Import[URL["https://oeis.org/A019505/b019505.txt"], "Data"]]
dataA241813 = Take[Map[First, Select[Map[{2#[[1]], 2#[[1]]==#[[2]]}&, Transpose[{Most[dataA019505], Rest[dataA019505]}]], !#[[2]]&]], 22] (* Hartmut F. W. Hoft, Feb 22 2023 *)

Extensions

More terms from Hartmut F. W. Hoft, Feb 22 2023