A080366 Numbers k whose least and greatest prime divisors are non-unitary.
4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 300, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576, 588, 600, 625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972
Offset: 1
Keywords
Examples
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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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}] -
PARI
isA080366(n) = e=factor(n)[,2];e&&e[1]>1&&e[#e]>1 \\ Jeppe Stig Nielsen, Jun 27 2017