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A133945 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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Every divisor of an odd integer is an "isolated divisor."

a(2n+1) = 2n+1; a(2n) = 2n - A133946(n) .

LINKS

Table of n, a(n) for n=1..73.

MATHEMATICA

g[n_] := Block[{d = Divisors[n]}, Select[d, FreeQ[d, # - 1] && FreeQ[d, # + 1] &]]; Table[Plus @@ EulerPhi /@ g[n], {n, 100}] (* Ray Chandler, May 28 2008 *)

CROSSREFS

Cf. A133946.

Sequence in context: A328579 A046524 A086571 * A124219 A103833 A226172

Adjacent sequences:  A133942 A133943 A133944 * A133946 A133947 A133948

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 30 2007

EXTENSIONS

Extended by Ray Chandler, May 28 2008

STATUS

approved

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)