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.

4, 8, 9, 18, 21, 25, 33, 49, 57, 69, 81, 85, 93, 121, 129, 133, 145, 169, 177, 205, 213, 217, 237, 249, 253, 265, 273, 289, 309, 361, 393, 417, 445, 469, 489, 493, 505, 517, 529, 553, 565, 573, 597, 633, 669, 685, 697, 753, 777, 781, 793, 813, 817, 841, 865

Offset: 1

Author

Enoch Haga, Jan 09 2004

Keywords

• easy
• nonn

Examples

			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.
		

References

• Glenn James and Robert C. James, Mathematics Dictionary, Princeton, N.J.: D. Van Nostrand Co., Inc., 1959; page 154 (factor of an integer).

Links

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

Crossrefs

Cf. A002808, A048968, A048969.

Programs

Mathematica

aQ[n_] := CompositeQ[n] && PrimeQ[(DivisorSigma[1, n] - n - 1)/(DivisorSigma[0, n] - 2)]; Select[Range[865], aQ] (* Amiram Eldar, Sep 07 2019 *)

Formula

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.