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 A030057 Least number that is not a sum of distinct divisors of n. 11
 2, 4, 2, 8, 2, 13, 2, 16, 2, 4, 2, 29, 2, 4, 2, 32, 2, 40, 2, 43, 2, 4, 2, 61, 2, 4, 2, 57, 2, 73, 2, 64, 2, 4, 2, 92, 2, 4, 2, 91, 2, 97, 2, 8, 2, 4, 2, 125, 2, 4, 2, 8, 2, 121, 2, 121, 2, 4, 2, 169, 2, 4, 2, 128, 2, 145, 2, 8, 2, 4, 2, 196, 2, 4, 2, 8, 2, 169, 2, 187, 2, 4, 2, 225, 2, 4, 2, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = 2 if and only if n is odd. a(2^n) = 2^(n+1). - Emeric Deutsch, Aug 07 2005 a(n) > n if and only if n belongs to A005153, and then a(n) = sigma(n) + 1. - Michel Marcus, Oct 18 2013 The most frequent values are 2 (50%), 4 (16.7%), 8 (5.7%), 13 (3.2%), 16 (2.4%), 29 (1.3%), 32 (1%), 40, 43, 61, ... - M. F. Hasler, Apr 06 2014 The indices of records occur at the highly abundant numbers, excluding 3 and 10, if Jaycob Coleman's conjecture at A002093 that all these numbers are practical numbers (A005153) is true. - Amiram Eldar, Jun 13 2020 LINKS David Wasserman and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 1000 terms from David Wasserman) EXAMPLE a(10)=4 because 4 is the least positive integer that is not a sum of distinct divisors (namely 1,2,5 and 10) of 10. MAPLE with(combinat): with(numtheory): for n from 1 to 100 do div:=powerset(divisors(n)): b[n]:=sort({seq(sum(div[i][j], j=1..nops(div[i])), i=1..nops(div))}) od: for n from 1 to 100 do B[n]:={seq(k, k=0..1+sigma(n))} minus b[n] od: seq(B[n], n=1..100); # Emeric Deutsch, Aug 07 2005 MATHEMATICA a[n_] :=  First[ Complement[ Range[ DivisorSigma[1, n] + 1], Total /@ Subsets[ Divisors[n]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 02 2012 *) PROG (Haskell) a030057 n = head \$ filter ((== 0) . p (a027750_row n)) [1..] where    p _      0 = 1    p []     _ = 0    p (k:ks) x = if x < k then 0 else p ks (x - k) + p ks x -- Reinhard Zumkeller, Feb 27 2012 CROSSREFS Cf. A002093, A005153, A093896, A119347. Distinct elements form A030058. Cf. A027750. Sequence in context: A059866 A278262 A093895 * A286596 A134066 A090988 Adjacent sequences:  A030054 A030055 A030056 * A030058 A030059 A030060 KEYWORD nonn,nice,look AUTHOR EXTENSIONS Edited by N. J. A. Sloane, May 05 2007 STATUS approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)