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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. 5
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

Table of n, a(n) for n=1..56.

EXAMPLE

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

MAPLE

with(numtheory): P:=proc(n) local a, k, ok; a:=ifactors(n)[2];

if nops(a)>1 then ok:=1; for k from 1 to nops(a)-1 do

  if a[k][2]<=a[k+1][2] then ok:=0; break; fi; od; fi;

if ok=1 then ok:=0; n; fi; end: seq(P(i), i=1..3*10^2);

# Paolo P. Lava, Jan 18 2018

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

CROSSREFS

Subset of A126706 and A097318 and A112769.

Cf. A097319, A230766.

Sequence in context: A316597 A329142 A112769 * A332956 A204825 A111592

Adjacent sequences:  A097317 A097318 A097319 * A097321 A097322 A097323

KEYWORD

nonn

AUTHOR

Ralf Stephan, Aug 04 2004

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)