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Search: id:A133946
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| A133946 |
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a(n) = Sum phi(k), where the sum is over the integers k which are the "non-isolated divisors" of 2n, and phi(k) is the Euler totient function (phi(k) = A000010(k)). A positive divisor k of n is non-isolated if k-1 and/ or k+1 also divides n. |
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2
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| 2, 2, 4, 2, 2, 6, 2, 2, 4, 8, 2, 6, 2, 2, 10, 2, 2, 6, 2, 8, 12, 2, 2, 6, 2, 2, 4, 12, 2, 12, 2, 2, 4, 2, 2, 16, 2, 2, 4, 8, 2, 14, 2, 2, 20, 2, 2, 6, 2, 8, 4, 2, 2, 6, 16, 12, 4, 2, 2, 12, 2, 2, 12, 2, 2, 20, 2, 2, 4, 8, 2, 16, 2, 2, 10, 2, 2, 22, 2, 8, 4, 2, 2, 18, 2, 2, 4, 2, 2, 22, 20, 2, 4, 2, 2, 6, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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No odd integer has any non-isolated divisors.
a(n) = 2n - A133945(2n).
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MATHEMATICA
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Table[Plus @@ EulerPhi[Select[Divisors[2n], If[ # > 1, IntegerQ[2n/(# - 1)]] || IntegerQ[2n/(# + 1)] &]], {n, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 04 2007
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CROSSREFS
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Cf. A133945.
Sequence in context: A118232 A115070 A064145 this_sequence A029640 A033722 A113200
Adjacent sequences: A133943 A133944 A133945 this_sequence A133947 A133948 A133949
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Oct 03 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 04 2007
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 28 2008
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