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Search: id:A132783
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| A132783 |
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Numbers n with the property that the difference between the two largest proper divisors of n equals the sum of proper divisors of the digit sum of n. |
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+0
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| 57, 5767, 6497, 7387, 29177, 30967, 35657, 37627, 52891, 53297, 61937, 70747, 75067, 96091, 114857, 118961, 126727, 145097, 190087, 194417, 215287, 221777, 244961, 307961, 335177, 348091, 370817, 408257, 414727, 423737, 462391, 585161
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All but two members of the sequence below 20000000 are the products of two primes separated by 6 or 16, and have digit sums of 25 or 26, which have proper divisor sums of 6 (=1+5) and 16(=1+2+13) respectively. The exceptions are the 1st term (57), which has a digit sum of 12, and the 67th (18999857), which has a digit sum of 56.
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EXAMPLE
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The divisors of 57 are 1, 3 and 19, so the difference of the two largest is 16.
The divisors of its digit sum (12=5+7) are 1,2,3,4 and 6, which also sum to 16.
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PROGRAM
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A program to test an individual integer, written in APL, is available if required.
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CROSSREFS
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Sequence in context: A122533 A015259 A012165 this_sequence A127455 A091749 A094777
Adjacent sequences: A132780 A132781 A132782 this_sequence A132784 A132785 A132786
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KEYWORD
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nonn,base
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AUTHOR
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Paul H. Smith (decisionbydesign(AT)aol.com), Nov 17 2007
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