A164830 a(1) = 2; a(n) for n > 1 is the smallest k > a(n-1) such that the arithmetic mean of the divisors of k is one of the previous terms a(1), ..., a(n-1).

2, 3, 5, 6, 11, 14, 15, 29, 38, 39, 44, 54, 56, 60, 107, 111, 125, 129, 142, 147, 153, 158, 159, 177, 187, 188, 198, 203, 209, 230, 238, 248, 255, 257, 266, 273, 276, 283, 285, 293, 297, 308, 317, 330, 353, 365, 373, 378, 420, 422, 438, 471, 485, 505, 509, 526

Offset

1,1

Comments

The arithmetic mean of the divisors of k is A000203(k)/A000005(k). a(n) for n > 1 is an arithmetic number, a term of A003601.

Similar sequences are obtained for other values of a(1). E.g. a(1) = 4 gives 4, 7, 13, 20, 45, 57, 89, 113, ... ; a(1) = 9 gives 9, 17, 22, 30, 43, 59, 87, 95, ... .

Links

Table of n, a(n) for n=1..56.

Example

The smallest number with arithmetic mean of divisors = 2 is 3, hence a(2) = 3.
The next number with arithmetic mean of divisors in {2, 3} is 5, hence a(3) = 5.
The smallest number > a(5) = 11 with arithmetic mean of divisors in {a(1), ..., a(5)} = {2, 3, 5, 6, 11} is 14, hence a(6) = 14.

Prog

(Magma) S:={2}; for n in [1..600] do q, r:=Quotrem(&+Divisors(n), NumberOfDivisors(n)); if r eq 0 and q in S then Include(~S, n); end if; end for; S; // Klaus Brockhaus, Sep 05 2009

Crossrefs

Cf. A000005 (tau, sigma_0, number of divisors), A000203 (sigma, sum of divisors), A003601 (arithmetic mean of divisors is an integer, arithmetic numbers).

Sequence in context: A329159 A350230 A104012 * A039037 A050049 A132581

Adjacent sequences: A164827 A164828 A164829 * A164831 A164832 A164833

Keyword

nonn

Author

Jaroslav Krizek, Aug 27 2009

Extensions

Edited and extended by Klaus Brockhaus, Sep 05 2009

Status

approved