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Search: id:A103826
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| A103826 |
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Unitary arithmetic numbers (those for which the arithmetic mean of the unitary divisors is an integer). |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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The arithmetic means of the unitary arithmetic numbers are in A103827.
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A103827, A034444, A034448.
Sequence in context: A031948 A165712 A161373 this_sequence A079905 A154611 A164028
Adjacent sequences: A103823 A103824 A103825 this_sequence A103827 A103828 A103829
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2005
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