A210510 Numbers not in the range of the sum of deficient divisors function.

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

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: A190329 A329791 A189522 * A050904 A263637 A347305

Adjacent sequences: A210507 A210508 A210509 * A210511 A210512 A210513

Keyword

nonn

Author

Timothy L. Tiffin, Jan 25 2013

Status

approved