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A304686
Numbers with strictly decreasing prime multiplicities.
11
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2018
STATUS
approved