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

1,1

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

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.

Example

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.

Mathematica

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

Crossrefs

Cf. A002808, A048968, A048969.

Sequence in context: A162898 A257009 A071592 * A116030 A116020 A354869

Adjacent sequences: A089762 A089763 A089764 * A089766 A089767 A089768

Keyword

easy,nonn

Author

Enoch Haga, Jan 09 2004

Status

approved