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A361386
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Infinitary arithmetic numbers: numbers for which the arithmetic mean of the infinitary divisors is an integer.
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3
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1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 22, 23, 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, 89, 91
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OFFSET
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1,2
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COMMENTS
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Subsequence of the unitary arithmetic numbers (A103826).
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LINKS
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FORMULA
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6 is a term since the arithmetic mean of its infinitary divisors, {1, 2, 3, 6}, is 3 which is an integer.
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MATHEMATICA
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f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, (1 + p^(2^(m - j)))/2, 1], {j, 1, m}]]; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], q]
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PROG
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(PARI) is(n) = {my(f = factor(n), b); denominator(prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], (f[i, 1]^(2^(#b-k))+1)/2, 1)))) == 1; }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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