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

Author

Olivier Gérard, Sep 23 2007

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

Extensions

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