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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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

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}]

Prog

(PARI) isA080366(n) = e=factor(n)[, 2]; e&&e[1]>1&&e[#e]>1 \\ Jeppe Stig Nielsen, Jun 27 2017

Crossrefs

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

Sequence in context: A341645 A339497 A348121 * A001694 A377821 A377846

Adjacent sequences: A080363 A080364 A080365 * A080367 A080368 A080369

Keyword

nonn

Author

Labos Elemer, Feb 21 2003

Status

approved