A133812 Numbers that are primally tight and have weakly descending powers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 23, 24, 25, 27, 29, 30, 31, 32, 35, 36, 37, 41, 43, 45, 47, 48, 49, 53, 59, 60, 61, 64, 67, 71, 72, 73, 77, 79, 81, 83, 89, 96, 97, 101, 103, 105, 107, 109, 113, 120, 121, 125, 127, 128, 131, 135, 137, 139, 143, 144

Offset

1,2

Comments

All numbers of the form p_1^k1*p_2^k2*...*p_n^k_n, where k1 >= k2 >= ... >= k_n and the p_i are n successive primes.

Differs from A073491 starting n=16.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

aQ[n_] := Module[{f=FactorInteger[n]}, p=f[[;; , 1]]; e=f[[;; , 2]]; PrimePi[p[[-1]]]-PrimePi[p[[1]]] == Length[p]-1 && AllTrue[Differences[e], #<=0 &]]; Join[{1}, Select[Range[2, 144], aQ]] (* Amiram Eldar, Jun 20 2019 *)

Crossrefs

Cf. A025487, A087980, A073491, A133808-A133813, A025487.

Sequence in context: A069899 A081306 A130073 * A115661 A318735 A002244

Adjacent sequences: A133809 A133810 A133811 * A133813 A133814 A133815

Keyword

nonn

Author

Olivier Gérard, Sep 23, 2007

Extensions

Cross-references from Charles R Greathouse IV, Dec 04 2009

Status

approved