A048751 Composites k whose product of divisors divided by number of divisors is an integer.

6, 8, 9, 10, 12, 14, 18, 22, 24, 26, 30, 34, 36, 38, 40, 42, 46, 54, 56, 58, 60, 62, 66, 70, 72, 74, 78, 80, 82, 84, 86, 88, 90, 94, 96, 102, 104, 106, 108, 110, 114, 118, 120, 122, 126, 128, 130, 132, 134, 136, 138, 142, 146, 150, 152, 154, 156, 158, 166, 168, 170

Offset: 1

Author

Enoch Haga, Dec 11 1999

Keywords

• easy
• nonn

Comments

Sequence is identical to A120736 except that it does not include terms 1 and 2, which are not composite. Michel Marcus, Jun 06 2014

Examples

			For k=8, product of divisors is 8*4*2*1=64; number of divisors = 4; 64/4 = 16 (an integer), so 8 is a term.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048747, A048752.

Programs

Mathematica

Select[Range[200],CompositeQ[#]&&IntegerQ[(Times@@Divisors[#])/ DivisorSigma[ 0,#]]&] (* Harvey P. Dale, Aug 21 2021 *)

PARI

isok(n) = (n!=1) && ! isprime(n) && (d = divisors(n)) && ((prod(i=1, #d, d[i]) % numdiv(n)) == 0); \\ Michel Marcus, Jun 05 2014

PARI

is(n)=my(f=factor(n)); n>5 && !isprime(n) && if(gcd(f[,2])%2, n^(numdiv(f)/2), sqrtint(n)^numdiv(f))%numdiv(f)==0 \\ Charles R Greathouse IV, Jun 06 2014

Extensions

Corrected by Michel Marcus, Jun 05 2014