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

Author

Jaroslav Krizek, Jan 22 2012

Keywords

• nonn

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

Crossrefs

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

Programs

Magma

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

Formula

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

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

Extensions

Spurious term removed by Jaroslav Krizek, Nov 26 2014