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A103826 Unitary arithmetic numbers (those for which the arithmetic mean of the unitary divisors is an integer). 4
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.

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

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. A103827, A034444, A034448.

Sequence in context: A161373 A285510 A174415 * A079905 A154611 A189669

Adjacent sequences:  A103823 A103824 A103825 * A103827 A103828 A103829

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 17 2005

STATUS

approved

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Last modified February 21 16:44 EST 2018. Contains 299414 sequences. (Running on oeis4.)