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A048751
Composites k whose product of divisors divided by number of divisors is an integer.
3
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
Sequence in context: A062973 A070162 A030550 * A024321 A161186 A102106
KEYWORD
easy,nonn
AUTHOR
Enoch Haga, Dec 11 1999
EXTENSIONS
Corrected by Michel Marcus, Jun 05 2014
STATUS
approved