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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A048747, A048752.

Sequence in context: A062973 A070162 A030550 * A024321 A161186 A102106

Adjacent sequences: A048748 A048749 A048750 * A048752 A048753 A048754

Keyword

easy,nonn

Author

Enoch Haga, Dec 11 1999

Extensions

Corrected by Michel Marcus, Jun 05 2014

Status

approved