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A097320 Numbers with more than one prime factor and, in the ordered factorization, the exponent always decreases when read from left to right. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If n = Product_{k=1..m} p(k)^e(k), then m > 1, e(1) > e(2) > ... > e(m).
LINKS
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.
Sequence in context: A362620 A112769 A360253 * A332956 A204825 A111592
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 04 2004
STATUS
approved

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Last modified July 12 08:52 EDT 2024. Contains 374239 sequences. (Running on oeis4.)