

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



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
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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 A213015
Adjacent sequences: A089762 A089763 A089764 * A089766 A089767 A089768


KEYWORD

easy,nonn


AUTHOR

Enoch Haga, Jan 09 2004


STATUS

approved



