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 A048146 Sum of non-unitary divisors of n. 23
 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 Antti Karttunen, Table of n, a(n) for n = 1..65537 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} ] (* Second program: *) Table[DivisorSum[n, # &, ! CoprimeQ[#, n/#] &], {n, 91}] (* Michael De Vlieger, Nov 20 2017 *) 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, A048106, A048107, A048109, A048111, A005117. Sequence in context: A158360 A094315 A212148 * A028973 A066503 A057385 Adjacent sequences:  A048143 A048144 A048145 * A048147 A048148 A048149 KEYWORD nonn AUTHOR EXTENSIONS Edited by Jaroslav Krizek, Mar 01 2009 STATUS approved

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Last modified January 17 17:13 EST 2018. Contains 297822 sequences.