A304686 Numbers with strictly decreasing prime multiplicities.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 37, 40, 41, 43, 44, 45, 47, 48, 49, 52, 53, 56, 59, 61, 63, 64, 67, 68, 71, 72, 73, 76, 79, 80, 81, 83, 88, 89, 92, 96, 97, 99, 101, 103, 104, 107, 109, 112, 113, 116, 117, 121

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 28 2021

Example

10 = 2*5 has prime multiplicities (1,1) so is not in the sequence.
20 = 2*2*5 has prime multiplicities (2,1) so is in the sequence
90 = 2*3*3*5 has prime multiplicities (1,2,1) so is not in the sequence.

Mathematica

Select[Range[200], Greater@@FactorInteger[#][[All, 2]]&]

Prog

(PARI) isok(n) = my(vm = factor(n)[, 2]); vm == vecsort(vm, , 4) && (#vm == #Set(vm)); \\ Michel Marcus, May 17 2018
(PARI) list(lim)=my(v=List()); forfactored(n=1, lim\1, if(n[2][, 2]==vecsort(n[2][, 2], , 8), listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Oct 28 2021

Crossrefs

Cf. A001221, A001222, A001597, A005117, A055932, A071365, A112769, A130091, A133808, A133811, A181819, A242031, A304678, A304679, A283050.

Sequence in context: A231876 A334298 A364160 * A354921 A085233 A357861

Adjacent sequences: A304683 A304684 A304685 * A304687 A304688 A304689

Keyword

nonn

Author

Gus Wiseman, May 16 2018

Status

approved