A063085 - OEIS

A063085

a(n) = usigma(n) - (phi(n) + d(n)), where usigma(n) is the sum of the unitary divisors of n and d(n) is the number of divisors of n.

-1, 0, 0, 0, 0, 6, 0, 1, 1, 10, 0, 10, 0, 14, 12, 4, 0, 18, 0, 16, 16, 22, 0, 20, 3, 26, 6, 22, 0, 56, 0, 11, 24, 34, 20, 29, 0, 38, 28, 30, 0, 76, 0, 34, 30, 46, 0, 42, 5, 52, 36, 40, 0, 58, 28, 40, 40, 58, 0, 92, 0, 62, 38, 26, 32, 116, 0, 52, 48, 112, 0, 54, 0, 74, 58, 58, 32, 136, 0, 60, 23, 82, 0, 124, 40, 86, 60, 60, 0, 144, 36, 70, 64

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OFFSET

1,6

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_] := Module[{f = FactorInteger[n]}, Times @@ (1 + Power @@@ f) - Times @@ (((#[[1]] - 1)*#[[1]]^(#[[2]] - 1)) & /@ f) - Times @@ (1 + f[[;; , 2]])]; a[1] = -1; Array[a, 100] (* Amiram Eldar, Mar 10 2026 *)

PROG

(PARI) a(n)={sumdiv(n, d, if(gcd(d, n/d)==1, d)) - eulerphi(n) - numdiv(n)}

CROSSREFS

Cf. A000005, A000010, A034448.

Sequence in context: A293299 A293486 A195398 * A020796 A011253 A388578

Adjacent sequences: A063082 A063083 A063084 * A063086 A063087 A063088

KEYWORD

easy,sign

AUTHOR

Jason Earls, Aug 06 2001

STATUS

approved