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

Author

Timothy L. Tiffin, Jan 25 2013

Keywords

• nonn

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

Crossrefs

Cf. A005100, A187793, A274829 (complement).

Programs

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 *)

PARI

v=vector(10^7); for(i=1, 10^7, if(sigma(i)Donovan Johnson, Feb 20 2013 */