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A055654 Difference between n and the result of "Phi-summation" over unitary divisors of n. 3
0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 0, 3, 0, 0, 0, 7, 0, 4, 0, 5, 0, 0, 0, 9, 4, 0, 8, 7, 0, 0, 0, 15, 0, 0, 0, 15, 0, 0, 0, 15, 0, 0, 0, 11, 10, 0, 0, 21, 6, 8, 0, 13, 0, 16, 0, 21, 0, 0, 0, 15, 0, 0, 14, 31, 0, 0, 0, 17, 0, 0, 0, 37, 0, 0, 12, 19, 0, 0, 0, 35, 26, 0, 0, 21, 0, 0, 0, 33, 0, 20, 0, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n - Sum_{u|n, gcd(u,n/u) = 1} phi(u), i.e. when u is a unitary divisor of n.

EXAMPLE

Squarefree numbers are roots of a(n)=0 equation, while Min n for which a(n)=k is k^2. See also A000188, A008833.

MATHEMATICA

Table[n - DivisorSum[n, EulerPhi[#] &, CoprimeQ[#, n/#] &], {n, 92}] (* Michael De Vlieger, Oct 26 2017 *)

PROG

(Haskell)

a055654 n = a055654_list !! (n-1)

a055654_list = zipWith (-) [1..] a055653_list

-- Reinhard Zumkeller, Mar 11 2012

(PARI) a(n) = n - sumdiv(n, d, if (gcd(d, n/d)==1, eulerphi(d))); \\ Michel Marcus, Oct 27 2017

CROSSREFS

Cf. A000188, A008833, A055653, A053570, A053571, A055631, A055632.

Sequence in context: A245203 A133949 A139808 * A170849 A292260 A322114

Adjacent sequences:  A055651 A055652 A055653 * A055655 A055656 A055657

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 07 2000

STATUS

approved

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Last modified January 21 17:43 EST 2019. Contains 319350 sequences. (Running on oeis4.)