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A048146 Sum of non-unitary divisors of n. 22
0, 0, 0, 2, 0, 0, 0, 6, 3, 0, 0, 8, 0, 0, 0, 14, 0, 9, 0, 12, 0, 0, 0, 24, 5, 0, 12, 16, 0, 0, 0, 30, 0, 0, 0, 41, 0, 0, 0, 36, 0, 0, 0, 24, 18, 0, 0, 56, 7, 15, 0, 28, 0, 36, 0, 48, 0, 0, 0, 48, 0, 0, 24, 62, 0, 0, 0, 36, 0, 0, 0, 105, 0, 0, 20, 40, 0, 0, 0, 84, 39, 0, 0, 64, 0, 0, 0, 72, 0, 54, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..91.

FORMULA

a(n) = A000203[n] - A034448[n] = sigma(n) - usigma(n). a(1) = 0, a(p) = 0, a(pq) = 0, a(pq...z) = 0, a(p^k) = (p^k - p) / (p - 1), for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k >=2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1) k = natural numbers (A000027).

EXAMPLE

If n = 1000, the 12 non-unitary divisors are {2, 4, 5, 10, 20, 25, 40, 50, 100, 200, 250, 500} and their sum is a[ n ] = a[ 1000 ] = 1206. a(16) = a(2^4) = (2^4 - 2) / (2 - 1)= 14.

MATHEMATICA

us[n_Integer] := (d = Divisors[n]; l = Length[d]; k = 1; s = n; While[k < l, If[ GCD[ d[[k]], n/d[[k]] ] == 1, s = s + d[[k]]]; k++ ]; s); Table[ DivisorSigma[1, n] - us[n], {n, 1, 100} ]

PROG

(PARI) a(n)=my(f=factor(n)); sigma(f)-prod(i=1, #f~, f[i, 1]^f[i, 2]+1) \\ Charles R Greathouse IV, Jun 17 2015

CROSSREFS

Cf. A034444, A000203, A048105-A048107, A048109, A048111, A005117.

Sequence in context: A158360 A094315 A212148 * A028973 A066503 A057385

Adjacent sequences:  A048143 A048144 A048145 * A048147 A048148 A048149

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

Edited by Jaroslav Krizek, Mar 01 2009

STATUS

approved

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Last modified September 23 21:16 EDT 2017. Contains 292391 sequences.