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, 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

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: A046524 A086571 A350509 * 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