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Search: id:A101223
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| A101223 |
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Numbers n whose deficiency is 10. |
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+0
2
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OFFSET
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1,1
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COMMENT
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Or, numbers n which satisfy g[n] := 2n+1-sigma[n] = 11.
Call a number which satisfies the equation g[n]:=2n+1-sigma[n]=x cofacient (from latin "co" and "facient" - "look") numbers of type x. It's easy to see that the perfect numbers are cofacient of type 1, the numbers 2^N are cofacient of type 2 (it is an open question whether there can be cofacient numbers of type 2 which are not powers of 2) and all prime numbers p are cofacient of type p (g[p]=p)
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LINKS
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V. K. Tintschev, Cofacient numbers.
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EXAMPLE
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68 is a term of the sequence because 2*2*17=68 and 68-34-17-4-2=g[68]=11
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MATHEMATICA
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Select[ Range[ 85000000], DivisorSigma[1, # ] + 10 == 2# &]
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CROSSREFS
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Sequence in context: A105956 A050718 A125164 this_sequence A109686 A077522 A049201
Adjacent sequences: A101220 A101221 A101222 this_sequence A101224 A101225 A101226
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KEYWORD
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nonn,more
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AUTHOR
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Vassil K. Tintschev (tinchev(AT)sunhe.jinr.ru), Dec 15 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 15 2004. No other terms below 56*10^7.
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