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Search: id:A133945
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| A133945 |
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Sum phi(k), where the sum is over the integers k which are the "isolated divisors" of n, and phi(k) is the Euler totient function (phi(k) = A000010(k)). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n. |
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+0
2
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| 1, 0, 3, 2, 5, 2, 7, 6, 9, 8, 11, 6, 13, 12, 15, 14, 17, 14, 19, 12, 21, 20, 23, 18, 25, 24, 27, 26, 29, 20, 31, 30, 33, 32, 35, 30, 37, 36, 39, 32, 41, 30, 43, 42, 45, 44, 47, 42, 49, 48, 51, 50, 53, 50, 55, 44, 57, 56, 59, 48, 61, 60, 63, 62, 65, 62, 67, 66, 69, 68, 71, 56, 73
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OFFSET
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1,3
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COMMENT
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Every divisor of an odd integer is an "isolated divisor."
a(2n+1) = 2n+1; a(2n) = 2n - A133946(n) .
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MATHEMATICA
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g[n_] := Block[{d = Divisors[n]}, Select[d, FreeQ[d, # - 1] && FreeQ[d, # + 1] &]]; Table[Plus @@ EulerPhi /@ g[n], {n, 100}] (*Chandler*)
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CROSSREFS
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Cf. A133946.
Sequence in context: A046524 A105222 A086571 this_sequence A124219 A103833 A046227
Adjacent sequences: A133942 A133943 A133944 this_sequence A133946 A133947 A133948
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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), Sep 30 2007
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 28 2008
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