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A228947 a(n) = sigma(n) - phi(n) - n. 2
-1, 0, -1, 1, -3, 4, -5, 3, -2, 4, -9, 12, -11, 4, 1, 7, -15, 15, -17, 14, -1, 4, -21, 28, -14, 4, -5, 16, -27, 34, -29, 15, -5, 4, -11, 43, -35, 4, -7, 34, -39, 42, -41, 20, 9, 4, -45, 60, -34, 23, -11, 22, -51, 48, -23, 40, -13, 4, -57, 92, -59 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

While terms with even indices are never negative, this is the case for most terms with odd indices; exceptions are listed in A229978.

LINKS

Table of n, a(n) for n=1..61.

Douglas E. Iannucci, On the Equation sigma(n) = n + phi(n), Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.2.

FORMULA

a(n) = 0  <=>  n = 2 (conjectured).

a(2n) > 0  for all n > 1.

a(2n+1) > 0  <=>  n in A229978.

a(n) = A051612(n) - n = A000203(n) - A000010(n) - n.

a(p) = 2 - p for p prime. - Alonso del Arte, Oct 05 2013

MATHEMATICA

Table[DivisorSigma[1, n] - EulerPhi[n] - n, {n, 75}] (* Alonso del Arte, Oct 05 2013 *)

PROG

(PARI) A228947(n)=sigma(n)-eulerphi(n)-n

CROSSREFS

Sequence in context: A099120 A199620 A016553 * A163874 A165565 A033706

Adjacent sequences:  A228944 A228945 A228946 * A228948 A228949 A228950

KEYWORD

sign

AUTHOR

M. F. Hasler, Oct 05 2013

STATUS

approved

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Last modified July 14 19:48 EDT 2020. Contains 335729 sequences. (Running on oeis4.)