A280946 Numbers n such that n and number of proper divisors (A032741) of n are relatively prime and n is a nonprime (A018252).

1, 8, 9, 10, 12, 14, 18, 22, 24, 25, 26, 28, 30, 32, 34, 35, 38, 40, 44, 46, 49, 52, 54, 55, 58, 60, 62, 63, 65, 66, 68, 72, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 94, 95, 96, 98, 99, 102, 104, 106, 108, 110, 112, 114, 115, 116, 117, 118, 119, 121, 122, 124, 125, 126, 128, 130, 133, 134, 135, 136, 138

Offset: 1

Author

Ilya Gutkovskiy, Jan 11 2017

Keywords

• nonn
• easy

Comments

Numbers n such that A125168(n) = 1 and A010051(n) = 0.

Numbers n such that gcd(n,A032741(n)) = 1 and A000005(n) != 2.

Examples

			12 is in the sequence because 12 is a nonprime, 12 has 5 proper divisors {1, 2, 3, 4, 6} and gcd(12,5) = 1.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A000005, A003624, A010051, A014567, A032741, A046642, A125168.

Programs

Mathematica

Select[Range[139], CoprimeQ[#1, DivisorSigma[0, #1] - 1] && !PrimeQ[#1] & ]
Select[Range[139], GCD[#1, DivisorSigma[0, #1] - 1] == 1 && DivisorSigma[0, #1] != 2 &]

PARI

isok(n) = gcd(n, numdiv(n)-1) == 1; \\ Michel Marcus, Jan 14 2017