A080366 - OEIS

%I #19 Sep 22 2019 07:52:13

%S 4,8,9,16,25,27,32,36,49,64,72,81,100,108,121,125,128,144,169,196,200,

%T 216,225,243,256,288,289,300,324,343,361,392,400,432,441,484,500,512,

%U 529,576,588,600,625,648,675,676,729,784,800,841,864,900,961,968,972

%N Numbers k whose least and greatest prime divisors are non-unitary.

%H Amiram Eldar, <a href="/A080366/b080366.txt">Table of n, a(n) for n = 1..10000</a>

%e n=300: it is not a prime, 300 = 2*2*3*5*5; extremal prime factors are 2 and 5; gcd(2, 300/2) > 1 and gcd(5, 300/5) > 1, so neither 2 nor 5 is a unitary prime divisor of 300, thus 300 is in this sequence. - _Labos Elemer_, corrected by _Jeppe Stig Nielsen_, Jun 27 2017

%t ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] mi[x_] := Part[Flatten[FactorInteger[x]], 1] k=0; Do[s=mi[n]; s1=ma[n]; If[ !Equal[GCD[s, n/s], 1]&&!Equal[GCD[s1, n/s1], 1]&&!PrimeQ[n], Print[n]], {n, 2, 1000}]

%o (PARI) isA080366(n) = e=factor(n)[,2];e&&e[1]>1&&e[#e]>1 \\ _Jeppe Stig Nielsen_, Jun 27 2017

%Y Cf. A006530, A020639, A034444, A056169, A080363, A080364, A080365.

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 21 2003