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Search: id:A152216
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| A152216 |
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For two consecutive numbers, the sum of the divisors of the sum of the two numbers divides the sum of the divisors of the product of the numbers. That is, numbers n such that sigma(2n+1)|sigma(n^2 + n) |
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1
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| 2, 5, 7, 11, 19, 20, 23, 28, 29, 32, 34, 38, 39, 41, 46, 53, 57, 59, 62, 70, 73, 77, 83, 89, 90, 94, 103, 104, 113, 118, 119, 124, 131, 160, 173, 177, 179, 188, 190, 191, 208, 227, 229, 233, 239, 242, 248, 251, 263, 280, 281, 290, 293, 297, 298, 311, 316, 327, 335
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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For n=11, 11+12=23, sigma(23)=24. Sigma(11*12)=sigma(132)=336 and 24|336
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MAPLE
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for n from 1 to 500 do if numtheory[sigma](n*(n+1)) mod numtheory[sigma](2*n+1) = 0 then printf("%d, ", n); fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 04 2008]
with(numtheory): a := proc (n) if type(sigma(n^2+n)/sigma(2*n+1), integer) = true then n else end if end proc: seq(a(n), n = 1 .. 400); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 03 2008]
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CROSSREFS
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Sequence in context: A163695 A134641 A162491 this_sequence A045350 A045351 A051645
Adjacent sequences: A152213 A152214 A152215 this_sequence A152217 A152218 A152219
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Nov 29 2008
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EXTENSIONS
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Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 03 2008
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