

A103827


Arithmetic means of the divisors of unitary arithmetic numbers (i.e., of those for which the arithmetic mean of the unitary divisors is an integer, A103826).


4



1, 2, 3, 3, 4, 5, 6, 5, 7, 6, 6, 9, 10, 8, 9, 12, 9, 13, 14, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, 15, 15, 18, 24, 17, 25, 18, 27, 21, 18, 18, 20, 30, 15, 31, 24, 20, 21, 18, 34, 24, 18, 36, 37, 26, 25, 24, 21, 40, 41, 42, 20, 27, 33, 30, 27, 45, 28, 30, 32, 36, 30, 33, 49
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OFFSET

1,2


COMMENTS

The unitary arithmetic numbers are in A103826.


LINKS

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


FORMULA

a(n) = A034448(A103826(n))/A034444(A103826(n)).  Amiram Eldar, Jun 19 2019


EXAMPLE

a(8) = 5 because the eighth unitary arithmetic number is A103826(8) = 12, the unitary divisors of 12 are 1, 3, 4 and 12 and (1 + 3 + 4 + 12)/4 = 5.


MAPLE

with(numtheory):unitdiv:=proc(n) local A, k: A:={}: for k from 1 to tau(n) do if gcd(divisors(n)[k], n/divisors(n)[k])=1 then A:=A union {divisors(n)[k]} else A:=A fi od end:utau:=n>nops(unitdiv(n)):usigma:=n>add(unitdiv(n)[j], j=1..nops(unitdiv(n))): p:=proc(n) if type(usigma(n)/utau(n), integer)=true then usigma(n)/utau(n) else fi end:seq(p(n), n=1..109);


MATHEMATICA

Select[Table[Mean[Select[Divisors[n], GCD[#, n/#]==1&]], {n, 150}], IntegerQ] (* Harvey P. Dale, May 20 2012 *)


CROSSREFS

Cf. A034444, A034448, A103826.
Sequence in context: A022290 A344350 A185363 * A094182 A300587 A075699
Adjacent sequences: A103824 A103825 A103826 * A103828 A103829 A103830


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Feb 17 2005


STATUS

approved



