The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A103826 Unitary arithmetic numbers (those for which the arithmetic mean of the unitary divisors is an integer). 11
 1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The arithmetic means of the unitary arithmetic numbers are in A103827. From Amiram Eldar, Mar 10 2023: (Start) Union of the odd numbers (A005408) and twice the numbers that are not the sum of 2 squares (A022544). The asymptotic density of this sequence is 1. (End) LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 12 is a unitary arithmetic number because the unitary divisors of 12 are 1,3,4 and 12 and (1+3+4+12)/4=5 is an integer. 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 n else fi end:seq(p(n), n=1..103); MATHEMATICA udiQ[n_]:=IntegerQ[Mean[Select[Divisors[n], GCD[#, n/#]==1&]]]; Select[ Range[ 100], udiQ] Harvey P. Dale, May 20 2012 Select[Range[100], IntegerQ[Times @@ ((1 + Power @@@ FactorInteger[#])/2)] &] (* Amiram Eldar, Jun 14 2022 *) PROG (PARI) is(n)=my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2]+1)%2^#f~==0 \\ Charles R Greathouse IV, Sep 01 2015 CROSSREFS Cf. A005408, A022544, A103827, A034444, A034448. Sequence in context: A285510 A174415 A356844 * A361386 A361786 A079905 Adjacent sequences: A103823 A103824 A103825 * A103827 A103828 A103829 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 17 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)