This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205099 #15 Feb 16 2025 08:33:16 %S A205099 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 A205099 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 A205099 1,40,49,64,19,1,40,44,1,23,46,33,1,21,76,35,50 %N A205099 Sum of proper divisors (A001065) of deficient numbers (A005100). %H A205099 Michael De Vlieger, <a href="/A205099/b205099.txt">Table of n, a(n) for n = 1..10000</a> %H A205099 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a> %H A205099 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a> %F A205099 a(n) = 1 for A005100(n) = prime. %F A205099 a(n) = A001065(A005100(n)) = A204823(n) - A005100(n). %t A205099 a205099[n_Integer] := %t A205099 DivisorSigma[1, #] - # & /@ %t A205099 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 A205099 (Magma) [SumOfDivisors(n)- n: n in [1..1000] | SumOfDivisors(n) lt 2*n] %Y A205099 Cf. A205098 (sum of proper divisors of abundant numbers), A204823 (sum of divisors of deficient numbers). %K A205099 nonn %O A205099 1,4 %A A205099 _Jaroslav Krizek_, Jan 22 2012 %E A205099 Spurious term removed by _Jaroslav Krizek_, Nov 26 2014