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).

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

Offset: 1

Author

Emeric Deutsch, Feb 17 2005

Keywords

• nonn

Comments

The unitary arithmetic numbers are in A103826.

Examples

			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.
		

Links

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

Crossrefs

Cf. A034444, A034448, A103826.

Programs

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 *)
Select[Times @@ ((1 + Power @@@ FactorInteger[#])/2) & /@ Range[100], IntegerQ] (* Amiram Eldar, Jun 14 2022 *)

Formula

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