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A306927 a(n) = A001615(n) - n. 2
0, 1, 1, 2, 1, 6, 1, 4, 3, 8, 1, 12, 1, 10, 9, 8, 1, 18, 1, 16, 11, 14, 1, 24, 5, 16, 9, 20, 1, 42, 1, 16, 15, 20, 13, 36, 1, 22, 17, 32, 1, 54, 1, 28, 27, 26, 1, 48, 7, 40, 21, 32, 1, 54, 17, 40, 23, 32, 1, 84, 1, 34, 33, 32, 19, 78, 1, 40, 27, 74, 1, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Analogous to A051953.

a(n) = A051953(n) if n is an element of A000961.

a(n) > A051953(n) if n is an element of A024619.

The sum of the proper divisors d of n such that n/d is squarefree. - Amiram Eldar, Sep 06 2019

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Wikipedia, Dedekind psi function

FORMULA

a(n) = A001615(n) - n.

a(n) = Sum_{d|n, d<n} (mu(n/d)^2 * d). - Amiram Eldar, Sep 06 2019

EXAMPLE

0 is a term because A001615(1) - 1 = 0.

1 is a term because A001615(2) - 2 = 1.

3 is a term because A001615(9) - 9 = 3.

MATHEMATICA

a[1] = 0; a[n_] := n * (Times @@ (1 + 1/FactorInteger[n][[;; , 1]]) - 1); Array[a, 100] (* Amiram Eldar, Sep 06 2019 *)

PROG

(PARI) a(n) = n*(sumdivmult(n, d, issquarefree(d)/d) - 1); \\ Michel Marcus, Mar 18 2019

CROSSREFS

Cf. A000961, A001615, A024619, A051953.

Sequence in context: A306695 A242926 A189733 * A277791 A243146 A048671

Adjacent sequences:  A306924 A306925 A306926 * A306928 A306929 A306930

KEYWORD

nonn

AUTHOR

Torlach Rush, Mar 16 2019

STATUS

approved

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Last modified February 25 06:46 EST 2020. Contains 332220 sequences. (Running on oeis4.)