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Sum of proper divisors (A001065) of deficient numbers (A005100).
3

%I #14 Sep 08 2022 08:46:01

%S 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,

%T 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,

%U 1,40,49,64,19,1,40,44,1,23,46,33,1,21,76,35,50

%N Sum of proper divisors (A001065) of deficient numbers (A005100).

%H Michael De Vlieger, <a href="/A205099/b205099.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a>

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

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

%t a205099[n_Integer] :=

%t DivisorSigma[1, #] - # & /@

%t 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 *)

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

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

%K nonn

%O 1,4

%A _Jaroslav Krizek_, Jan 22 2012

%E Spurious term removed by _Jaroslav Krizek_, Nov 26 2014