cp's OEIS Frontend

A089765 Composite n whose sum of distinct divisors, s(d), ignoring divisors n and 1, divided by the count of divisors (not counting n and 1), c(d), are primes. Duplicate divisors, as in 2*2=4 are counted just once.

%I A089765 #12 Sep 07 2019 08:44:42
%S A089765 4,8,9,18,21,25,33,49,57,69,81,85,93,121,129,133,145,169,177,205,213,
%T A089765 217,237,249,253,265,273,289,309,361,393,417,445,469,489,493,505,517,
%U A089765 529,553,565,573,597,633,669,685,697,753,777,781,793,813,817,841,865
%N A089765 Composite n whose sum of distinct divisors, s(d), ignoring divisors n and 1, divided by the count of divisors (not counting n and 1), c(d), are primes. Duplicate divisors, as in 2*2=4 are counted just once.
%D A089765 Glenn James and Robert C. James, Mathematics Dictionary, Princeton, N.J.: D. Van Nostrand Co., Inc., 1959; page 154 (factor of an integer).
%H A089765 Amiram Eldar, <a href="/A089765/b089765.txt">Table of n, a(n) for n = 1..10000</a>
%F A089765 Factor n into its distinct divisors, ignore n and 1, add the divisors and divide by the number of divisors. If s(d) / c(d) [sum divided by count] is prime, add to sequence.
%e A089765 a(1)= 8 because its factors are 8, 1, 2, 4. Ignoring 8 and 1, the sum of 2+4=6. The count of factors is 2 and 6/2=3, a prime.
%t A089765 aQ[n_] := CompositeQ[n] && PrimeQ[(DivisorSigma[1, n] - n - 1)/(DivisorSigma[0, n] - 2)]; Select[Range[865], aQ] (* _Amiram Eldar_, Sep 07 2019 *)
%Y A089765 Cf. A002808, A048968, A048969.
%K A089765 easy,nonn
%O A089765 1,1
%A A089765 _Enoch Haga_, Jan 09 2004