A335029 Numbers that are not practical (A237287) and have more divisors than any smaller number that is not practical.

3, 9, 10, 44, 70, 225, 315, 770, 1575, 2835, 3465, 10010, 17325, 31185, 45045, 121275, 135135, 225225, 405405, 675675, 1576575, 2027025, 2297295, 3828825, 6891885, 11486475, 26801775, 34459425, 43648605, 72747675, 130945815, 218243025, 509233725, 654729075, 1003917915

Offset

1,1

Comments

The corresponding numbers of divisors are 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 96, 108, 120, 128, 144, 160, 192, 216, 240, 256, 288, 320, 384, 432, 480, 512, ...

Of the first 39 terms, 34 terms are also in A038547.

None of the terms are highly composite (A002182) since all the highly composite numbers are practical numbers (A005153).

Links

Table of n, a(n) for n=1..35.

Example

The first 5 numbers that are not practical are 3, 5, 7, 9, 10. Their numbers of divisors are 2, 2, 2, 3, 4. The record numbers of divisors are 2, 3 and 4 which occur at 3, 9 and 10.

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[fct_] := (ind = Position[fct[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), _?(# > 1 &)]) == {}; seq = {}; dm = 1; Do[fct = FactorInteger[n]; d = Times @@ (1 + Last/@ fct); If[d > dm && !pracQ[fct], dm = d; AppendTo[seq, n]], {n, 3, 10^5}]; seq

Crossrefs

Cf. A002182, A005153, A237287, A275239, A335008, A335030.

Sequence in context: A004669 A173242 A335030 * A228450 A121057 A025538

Adjacent sequences: A335026 A335027 A335028 * A335030 A335031 A335032

Keyword

nonn

Author

Amiram Eldar, May 20 2020

Status

approved