A048752 -id:A048752 - cp's OEIS frontend

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

Enoch Haga, Dec 11 1999

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

			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.

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

Cf. A048747, A048752.

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

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

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

Corrected by Michel Marcus, Jun 05 2014

A048753 Composite numbers k whose product of aliquot divisors divided by number of aliquot divisors is an integer.

Original entry on oeis.org

4, 6, 15, 16, 20, 21, 27, 33, 36, 39, 42, 45, 48, 50, 51, 56, 57, 69, 70, 75, 87, 93, 100, 105, 111, 120, 123, 129, 132, 141, 154, 159, 162, 175, 177, 182, 183, 189, 196, 198, 201, 210, 213, 219, 220, 231, 237, 238, 245, 249, 256, 266, 267, 270, 273, 275, 291

Offset: 1

Enoch Haga

			For k=6, the product of aliquot divisors is 3*2*1=6; the number of aliquot divisors is 3; 6/3 = 2 (an integer), so 6 is a term.

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

Cf. A007956, A032741, A048752, A048754.

padQ[n_]:=Module[{ad=Most[Divisors[n]]},!PrimeQ[n]&&Divisible[Times@@ad, Length[ad]]]; Select[Range[2,300],padQ] (* Harvey P. Dale, May 07 2012 *)

cp's OEIS Frontend

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

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