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A133946 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. 1
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No odd integer has any non-isolated divisors.

a(n) = 2n - A133945(2n).

LINKS

Table of n, a(n) for n=1..97.

MATHEMATICA

Table[Plus @@ EulerPhi[Select[Divisors[2n], If[ # > 1, IntegerQ[2n/(# - 1)]] || IntegerQ[2n/(# + 1)] &]], {n, 1, 80}] (* Stefan Steinerberger, Oct 04 2007 *)

CROSSREFS

Cf. A133945.

Sequence in context: A261891 A321320 A175462 * A286250 A278244 A278542

Adjacent sequences:  A133943 A133944 A133945 * A133947 A133948 A133949

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 03 2007

EXTENSIONS

More terms from Stefan Steinerberger, Oct 04 2007

Extended by Ray Chandler, May 28 2008

STATUS

approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)