A335029 - OEIS

%I #6 May 20 2020 07:40:18

%S 3,9,10,44,70,225,315,770,1575,2835,3465,10010,17325,31185,45045,

%T 121275,135135,225225,405405,675675,1576575,2027025,2297295,3828825,

%U 6891885,11486475,26801775,34459425,43648605,72747675,130945815,218243025,509233725,654729075,1003917915

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

%C 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, ...

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

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

%e 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.

%t 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

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

%K nonn

%O 1,1

%A _Amiram Eldar_, May 20 2020