A205099 Sum of proper divisors (A001065) of deficient numbers (A005100).

0, 1, 1, 3, 1, 1, 7, 4, 8, 1, 1, 10, 9, 15, 1, 1, 11, 14, 1, 6, 16, 13, 1, 1, 31, 15, 20, 13, 1, 22, 17, 1, 1, 40, 33, 26, 1, 8, 43, 21, 46, 1, 17, 23, 32, 1, 1, 34, 41, 63, 19, 1, 58, 27, 1, 1, 40, 49, 64, 19, 1, 40, 44, 1, 23, 46, 33, 1, 21, 76, 35, 50

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Restricted Divisor Function

Eric Weisstein's World of Mathematics, Deficient Number

Formula

a(n) = 1 for A005100(n) = prime.

a(n) = A001065(A005100(n)) = A204823(n) - A005100(n).

Mathematica

a205099[n_Integer] :=
DivisorSigma[1, #] - # & /@
Select[Range[n], DivisorSigma[1, #] < 2*# &]; a205099[94] (* Michael De Vlieger, Nov 26 2014, after Jean-François Alcover at A001065 and Stefan Steinerberger at A005100 *)

Prog

(Magma) [SumOfDivisors(n)- n: n in [1..1000] | SumOfDivisors(n) lt 2*n]

Crossrefs

Cf. A205098 (sum of proper divisors of abundant numbers), A204823 (sum of divisors of deficient numbers).

Sequence in context: A158198 A158793 A112996 * A136621 A108625 A112857

Adjacent sequences: A205096 A205097 A205098 * A205100 A205101 A205102

Keyword

nonn

Author

Jaroslav Krizek, Jan 22 2012

Extensions

Spurious term removed by Jaroslav Krizek, Nov 26 2014

Status

approved