A080364 -id:A080364 - cp's OEIS frontend

A080365 Composite numbers k whose smallest and largest prime factors are unitary prime factors.

6, 10, 14, 15, 21, 22, 26, 30, 33, 34, 35, 38, 39, 42, 46, 51, 55, 57, 58, 62, 65, 66, 69, 70, 74, 77, 78, 82, 85, 86, 87, 90, 91, 93, 94, 95, 102, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 126, 129, 130, 133, 134, 138, 141, 142, 143, 145, 146, 154, 155, 158

Offset: 1

Labos Elemer, Feb 21 2003

nonn

			k=90 is not a prime; 90 = 2*3*3*5; extremal prime factors are 2 and 5; gcd(2, 90/2) = gcd(5, 90/5) = 1, so 2 and 5 are unitary prime divisors of 90, thus 90 is in the sequence.

Muniru A Asiru, Table of n, a(n) for n = 1..3000

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

D:=List(Filtered([2..160],i->not IsPrime(i)),Factors);;
a:=[];;  for i in D do if Gcd(i[1],Product(i)/i[1])=1 and Gcd(i[Length(i)],Product(i)/i[Length(i)])=1 then Add(a,Product(i)); fi; od; a;  # Muniru A Asiru, Jul 10 2018~

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, 256}]

lista(nn) = {forcomposite(n=1, nn, my(f=factor(n)[,1], p = vecmin(f), q = vecmax(f)); if ((gcd(p, n/p) == 1) && (gcd(q, n/q) == 1), print1(n, ", ")););} \\ Michel Marcus, Jul 09 2018

A080366 Numbers k whose least and greatest prime divisors are non-unitary.

Original entry on oeis.org

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

Labos Elemer, Feb 21 2003

nonn

			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

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

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

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}]

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

cp's OEIS Frontend

A080365 Composite numbers k whose smallest and largest prime factors are unitary prime factors.

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