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

1,1

Comments

This sequence contains all unimodal composites (numbers whose list of prime factors is strictly increasing then strictly decreasing).

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

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).

Mathematica

Module[{pfl},
Select[Range[2000],
  Function[n, pfl = Power @@@ FactorInteger[n];
   1 < First[First[Position[pfl, Max[pfl], 1]]] < Length[pfl]]]]

Prog

(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

Crossrefs

Cf. A057715 (numbers with strictly decreasing prime power factor list).

Sequence in context: A396647 A114826 A332725 * A379093 A332831 A103653

Adjacent sequences: A253382 A253383 A253384 * A253386 A253387 A253388

Keyword

nonn,easy

Author

Olivier Gérard, Dec 30 2014

Status

approved