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 A080226 Number of deficient divisors of n. 9
 1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 2, 4, 2, 4, 4, 5, 2, 4, 2, 5, 4, 4, 2, 5, 3, 4, 4, 5, 2, 6, 2, 6, 4, 4, 4, 5, 2, 4, 4, 6, 2, 6, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 5, 4, 6, 4, 4, 2, 7, 2, 4, 6, 7, 4, 6, 2, 6, 4, 7, 2, 6, 2, 4, 6, 6, 4, 6, 2, 7, 5, 4, 2, 7, 4, 4, 4, 7, 2, 8, 4, 6, 4, 4, 4, 7, 2, 6, 6, 7, 2, 6, 2, 7, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of divisors d of n with sigma(d)<2*d (sigma = A000203). LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 Eric Weisstein's World of Mathematics, Deficient Number. FORMULA A080224(n) + A080225(n) + a(n) = A000005(n). a(n) = Sum_{d|n} A294934(d) = A294926(n) + A294934(n). - Antti Karttunen, Nov 14 2017 EXAMPLE All 4 divisors of n=21 are deficient: 1=A005100(1), 3=A005100(3), 7=A005100(6) and 21=A005100(17), therefore a(21)=4. MATHEMATICA a[n_] := Sum[If[DivisorSigma[1, d] < 2d, 1, 0], {d, Divisors[n]}]; Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *) PROG (PARI) A080226(n) = sumdiv(n, d, (sigma(d)<(2*d))); \\ Antti Karttunen, Nov 14 2017 CROSSREFS Cf. A000203, A005100, A187793, A294926, A294934. Sequence in context: A135615 A348856 A166469 * A060741 A125747 A060129 Adjacent sequences:  A080223 A080224 A080225 * A080227 A080228 A080229 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 07 2003 STATUS approved

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Last modified July 3 22:23 EDT 2022. Contains 355058 sequences. (Running on oeis4.)