login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335029 Numbers that are not practical (A237287) and have more divisors than any smaller number that is not practical. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 22:22 EST 2021. Contains 349589 sequences. (Running on oeis4.)