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A030057 Least number that is not a sum of distinct divisors of n. 8
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

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][1], 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-Fran├žois 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. A005153, A093896.

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

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, May 05 2007

STATUS

approved

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Last modified February 17 04:02 EST 2019. Contains 320201 sequences. (Running on oeis4.)