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Search: id:A126168
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| A126168 |
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Sum of the proper infinitary divisors of n. |
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+0
19
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| 0, 1, 1, 1, 1, 6, 1, 7, 1, 8, 1, 8, 1, 10, 9, 1, 1, 12, 1, 10, 11, 14, 1, 36, 1, 16, 13, 12, 1, 42, 1, 19, 15, 20, 13, 14, 1, 22, 17, 50, 1, 54, 1, 16, 15, 26, 1, 20, 1, 28, 21, 18, 1, 66, 17, 64, 23, 32, 1, 60, 1, 34, 17, 21, 19, 78, 1, 22, 27, 74, 1, 78, 1, 40, 29
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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A divisor of n is called infinitary if it is a product of divisors of the form p^{y_a 2^a}, where p^y is a prime power dividing n and sum_a y_a 2^a is the binary representation of y.
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LINKS
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Wesstein, E, Infinitary Divisor. definition.
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FORMULA
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a(n)=isigma(n)-n = A049417(n)-n
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EXAMPLE
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As the infinitary divisors of 240 are 1,3,5,15,16,48,80,240, we have a(240)=1+3+5+15+16+48+80=168
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MATHEMATICA
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ExponentList[n_Integer, factors_List] := {#, IntegerExponent[n, # ]} & /@ factors; InfinitaryDivisors[1] := {1}; InfinitaryDivisors[n_Integer?Positive] := Module[ { factors = First /@ FactorInteger[n], d = Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g] == g][ #, Last[ # ]]] & /@ Transpose[Last /@ ExponentList[ #, factors] & /@ d]], _?( And @@ # &), {1}]] ]] ] Null; properinfinitarydivisorsum[k_] := Plus @@ InfinitaryDivisors[k] - k; properinfinitarydivisorsum /@ Range[75]
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CROSSREFS
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Cf. A049417, A037445.
Adjacent sequences: A126165 A126166 A126167 this_sequence A126169 A126170 A126171
Sequence in context: A127778 A076714 A113811 this_sequence A028323 A137235 A021166
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KEYWORD
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easy,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Dec 21 2006
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