A097320 Numbers with more than one prime factor and, in the ordered factorization, the exponent always decreases when read from left to right.

12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 63, 68, 72, 76, 80, 88, 92, 96, 99, 104, 112, 116, 117, 124, 135, 136, 144, 148, 152, 153, 160, 164, 171, 172, 175, 176, 184, 188, 189, 192, 200, 207, 208, 212, 224, 232, 236, 244, 248, 261, 268, 272, 275, 279, 284, 288

Offset

1,1

Comments

If n = Product_{k=1..m} p(k)^e(k), then m > 1, e(1) > e(2) > ... > e(m).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

80 is 2^4 * 5^1 and 4>1, so 80 is in sequence.

Mathematica

fQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Length[f] > 1 && Max[Differences[f]] < 0]; Select[Range[2, 288], fQ] (* T. D. Noe, Nov 04 2013 *)

Prog

(PARI) for(n=1, 320, F=factor(n); t=0; s=matsize(F)[1]; if(s>1, for(k=1, s-1, if(F[k, 2]<=F[k+1, 2], t=1; break)); if(!t, print1(n", "))))
(PARI) is(n) = my(f = factor(n)[, 2]); #f > 1 && vecsort(f, , 12) == f \\ Rick L. Shepherd, Jan 17 2018
(Python)
from sympy import factorint
def ok(n):
    e = list(factorint(n).values())
    return 1 < len(e) == len(set(e)) and e == sorted(e, reverse=True)
print([k for k in range(289) if ok(k)]) # Michael S. Branicky, Dec 20 2021

Crossrefs

Subsequence of A126706, A097318, A112769. Supersequence of A096156.

Cf. A097319, A230766.

Sequence in context: A362620 A112769 A360253 * A332956 A204825 A111592

Adjacent sequences: A097317 A097318 A097319 * A097321 A097322 A097323

Keyword

nonn

Author

Ralf Stephan, Aug 04 2004

Status

approved