A205099 -id:A205099 - cp's OEIS frontend

A204823 Sum of divisors (A000203) of deficient numbers (A005100).

1, 3, 4, 7, 6, 8, 15, 13, 18, 12, 14, 24, 24, 31, 18, 20, 32, 36, 24, 31, 42, 40, 30, 32, 63, 48, 54, 48, 38, 60, 56, 42, 44, 84, 78, 72, 48, 57, 93, 72, 98, 54, 72, 80, 90, 60, 62, 96, 104, 127, 84, 68, 126, 96, 72, 74, 114, 124, 140, 96, 80, 121, 126, 84, 108, 132

Offset: 1

Jaroslav Krizek, Jan 22 2012

nonn

a(n) = A000203(A005100(n)) = A005100(n) + A205099(n).

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Deficient Number

Cf. A204822 (sum of divisors of abundant numbers), A205099 (sum of proper divisors of deficient numbers).

sddn[n_]:=Module[{s=DivisorSigma[1,n]},If[s<2n,s,0]]; DeleteCases[ sddn/@ Range[ 100],0] (* Harvey P. Dale, Jan 02 2015 *)

for(n=1,300,s=sigma(n);if(s<2*n,print1(s", "))) \\ Charles R Greathouse IV, Feb 19 2013

a(n) < 8n/3. - Charles R Greathouse IV, Feb 19 2013

A205098 Sum of proper divisors (A001065) of abundant numbers (A005101).

Original entry on oeis.org

16, 21, 22, 36, 42, 55, 50, 54, 76, 66, 64, 108, 78, 74, 123, 90, 106, 140, 92, 144, 156, 117, 114, 106, 172, 136, 126, 240, 186, 204, 150, 196, 259, 222, 236, 218, 201, 312, 186, 196, 366, 198, 316, 203, 270, 265, 300, 226, 366, 384, 284, 234, 280, 332, 312

Offset: 1

Jaroslav Krizek, Jan 22 2012

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Abundant Number.
Eric Weisstein's World of Mathematics, Restricted Divisor Function.

Cf. A205099 (sum of proper divisors of deficient numbers), A204822 (sum of divisors of abundant numbers), A001065, A005101.

f[n_] := Module[{s = DivisorSigma[1, n] - n}, If[s > n, s, Nothing]]; Array[f, 250] (* Amiram Eldar, Mar 11 2024 *)

a(n) = A001065(A005101(n)) = A204822(n) - A005101(n).

cp's OEIS Frontend

A204823 Sum of divisors (A000203) of deficient numbers (A005100).

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