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Search: id:A085844
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| A085844 |
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Numbers equal to a permutation (or rearrangement) of the digits of the sum of their proper divisors. Rearrangements which cause leading zeros are excluded. |
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3
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| 6, 28, 411, 496, 604, 1305, 3664, 4086, 4672, 4896, 5046, 7785, 8128, 8739, 9331, 14535, 16012, 18342, 18585, 19648, 20634, 21534, 21628, 22365, 25911, 27568, 28108, 29160, 29188, 31185, 32091, 32271, 34956, 35898, 35925, 36172, 37698
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Perfect numbers (A000396) are a subsequence. Perfect numbers are defined as numbers equal to the sum of their proper divisors. The numbers in this sequence are not perfect, but are "permutably perfect" since they are equal to a permutation of the sum of their proper divisors.
Note a(79)=195921, and a(80)=199251, and these are both permutations of each other. The same is true of a(90)=226944 and a(93)=244692.
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EXAMPLE
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604 is a term because the divisors of 64 are {1, 2, 4, 151, 302, 604} and 1+2+4+151+302 = 460.
16012 is included because it has the proper divisors 1, 2, 4, 4003, 8006. These divisors sum to 12016, which is a rearrangement of the digits of 16012.
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CROSSREFS
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Cf. A000396.
Sequence in context: A134872 A049603 A035527 this_sequence A083387 A104511 A138876
Adjacent sequences: A085841 A085842 A085843 this_sequence A085845 A085846 A085847
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 05 2003; corrected Jul 07 2003.
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