A097319 Numbers with more than one prime factor and, in the ordered factorization, the exponents are strictly increasing.
18, 50, 54, 75, 98, 108, 147, 162, 242, 245, 250, 324, 338, 363, 375, 486, 500, 507, 578, 605, 648, 686, 722, 845, 847, 867, 972, 1029, 1058, 1083, 1125, 1183, 1250, 1372, 1445, 1458, 1587, 1682, 1715, 1805, 1859, 1875, 1922, 1944, 2023, 2250
Offset: 1
Keywords
Examples
507 is 3^1*13^2, A001221(507)=2 and 1<2, so 507 is in sequence. 150 is 2^1*3^1*5^2 is not in the sequence because 1,1,2 is not strictly increasing (although it is nondecreasing).
Links
- T. D. Noe, Table of n, a(n) for n = 1..1180
Programs
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Mathematica
fQ[n_] := Module[{d, f = FactorInteger[n]}, If[Length[f] == 1, False, d = Differences[Transpose[f][[2]]]; And @@ ((# > 0) & /@ d)]]; Select[Range[2250], fQ] (* T. D. Noe, Apr 09 2013 *) -
PARI
for(n=1, 3000, 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", "))))
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PARI
is(n) = my(f = factor(n)[,2]); #f > 1 && vecsort(f, , 8) == f \\ Rick L. Shepherd, Jan 17 2018
Comments