cp's OEIS Frontend

A253385 Numbers divisible by at least three distinct primes whose largest prime power factor is not based on its smallest nor its greatest prime factor.

%I A253385 #15 Jun 02 2025 13:26:06
%S A253385 90,126,180,252,270,350,360,378,504,525,540,550,594,630,650,700,702,
%T A253385 756,810,825,850,918,950,975,1026,1050,1078,1080,1100,1134,1150,1188,
%U A253385 1242,1260,1274,1275,1300,1350,1400,1404,1425,1512,1575,1617,1620,1650,1666,1700,1725,1750,1782,1836,1862,1890,1900,1911,1950
%N A253385 Numbers divisible by at least three distinct primes whose largest prime power factor is not based on its smallest nor its greatest prime factor.
%C A253385 This sequence contains all unimodal composites (numbers whose list of prime factors is strictly increasing then strictly decreasing).
%H A253385 David A. Corneth, <a href="/A253385/b253385.txt">Table of n, a(n) for n = 1..10000</a>
%e A253385 90 is the first member of this sequence because its prime factor decomposition is 2*3^2*5, using the three smallest primes and 3^2 = 9 is the first power of 3 greater than 5 (and 2).
%t A253385 Module[{pfl},
%t A253385 Select[Range[2000],
%t A253385   Function[n, pfl = Power @@@ FactorInteger[n];
%t A253385    1 < First[First[Position[pfl, Max[pfl], 1]]] < Length[pfl]]]]
%o A253385 (PARI) is(n) = {my(f=factor(n)); if(#f~<3, return(0)); t=max(f[1,1]^f[1,2], f[#f~,1]^f[#f~,2]); for(i=2, #f~, if(f[i, 1] ^ f [i, 2] > t, return(1))) ;0} \\ _David A. Corneth_, Jun 01 2025
%Y A253385 Cf. A057715 (numbers with strictly decreasing prime power factor list).
%K A253385 nonn,easy
%O A253385 1,1
%A A253385 _Olivier Gérard_, Dec 30 2014