cp's OEIS Frontend

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

%I A048751 #23 Aug 21 2021 12:14:46
%S A048751 6,8,9,10,12,14,18,22,24,26,30,34,36,38,40,42,46,54,56,58,60,62,66,70,
%T A048751 72,74,78,80,82,84,86,88,90,94,96,102,104,106,108,110,114,118,120,122,
%U A048751 126,128,130,132,134,136,138,142,146,150,152,154,156,158,166,168,170
%N A048751 Composites k whose product of divisors divided by number of divisors is an integer.
%C A048751 Sequence is identical to A120736 except that it does not include terms 1 and 2, which are not composite. _Michel Marcus_, Jun 06 2014
%H A048751 Charles R Greathouse IV, <a href="/A048751/b048751.txt">Table of n, a(n) for n = 1..10000</a>
%e A048751 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.
%t A048751 Select[Range[200],CompositeQ[#]&&IntegerQ[(Times@@Divisors[#])/ DivisorSigma[ 0,#]]&] (* _Harvey P. Dale_, Aug 21 2021 *)
%o A048751 (PARI) isok(n) = (n!=1) && ! isprime(n) && (d = divisors(n)) && ((prod(i=1, #d, d[i]) % numdiv(n)) == 0); \\ _Michel Marcus_, Jun 05 2014
%o A048751 (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
%Y A048751 Cf. A048747, A048752.
%K A048751 easy,nonn
%O A048751 1,1
%A A048751 _Enoch Haga_, Dec 11 1999
%E A048751 Corrected by _Michel Marcus_, Jun 05 2014