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.
90, 126, 180, 252, 270, 350, 360, 378, 504, 525, 540, 550, 594, 630, 650, 700, 702, 756, 810, 825, 850, 918, 950, 975, 1026, 1050, 1078, 1080, 1100, 1134, 1150, 1188, 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
Offset: 1
Examples
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).
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A057715 (numbers with strictly decreasing prime power factor list).
Programs
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Mathematica
Module[{pfl}, Select[Range[2000], Function[n, pfl = Power @@@ FactorInteger[n]; 1 < First[First[Position[pfl, Max[pfl], 1]]] < Length[pfl]]]] -
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
Comments