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A210510 Numbers not in the range of the sum of deficient divisors function. 2
2, 5, 9, 11, 16, 17, 21, 23, 25, 26, 29, 33, 35, 37, 39, 41, 45, 47, 49, 50, 51, 53, 55, 58, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 82, 83, 85, 87, 88, 89, 91, 95, 99, 100, 101, 103, 107, 109, 111, 113, 115, 116, 117, 119, 125, 129, 131, 136, 137, 141, 143, 145, 146, 147, 149, 155, 157, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers which do not appear in A187793 or in A274829; that is, there is no integer N whose sum of deficient divisors is equal to a(n) for any n.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

MATHEMATICA

sdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &]; ric[n_, lap_] := Block[{s, m, p = NextPrime@lap}, m = n*p; While[(s = sdef@m) <= Lim, T[[s]] = 1; ric[m, p]; m *= p; While[(s = sdef@m) <= Lim, T[[s]] = 1; ric[m, p]; m *= p]; p = NextPrime@p; m = n*p]]; seqTo[n_] := (Lim = n; T = 0 Range[n]; T[[1]] = 1; ric[1, 1]; Flatten@Position[T, 0]); seqTo[159] (* Giovanni Resta, Feb 20 2013 *)

PROG

(PARI) v=vector(10^7); for(i=1, 10^7, if(sigma(i)<i+i, v[i]=1)); m=vector(1799); for(i=1, 10^7, d=divisors(i); s=1; for(j=2, numdiv(i), if(v[d[j]]==1, s=s+d[j])); if(s<=1799, m[s]=1)); c=0; for(i=1, 1799, if(m[i]==0, c++; write("b210510.txt", c " " i))) /* Donovan Johnson, Feb 20 2013 */

CROSSREFS

Cf. A005100, A187793, A274829 (complement).

Sequence in context: A067568 A190329 A189522 * A050904 A263637 A057471

Adjacent sequences:  A210507 A210508 A210509 * A210511 A210512 A210513

KEYWORD

nonn

AUTHOR

Timothy L. Tiffin, Jan 25 2013

STATUS

approved

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Last modified September 18 05:32 EDT 2019. Contains 327165 sequences. (Running on oeis4.)