A274793 -id:A274793 - cp's OEIS frontend

A274790 Numbers in the range of the sum of odd divisors function.

1, 4, 6, 8, 12, 13, 14, 18, 20, 24, 30, 31, 32, 38, 40, 42, 44, 48, 54, 56, 57, 60, 62, 68, 72, 74, 78, 80, 84, 90, 96, 98, 102, 104, 108, 110, 112, 114, 120, 121, 124, 128, 132, 133, 138, 140, 144, 150, 152, 156, 158, 160, 164, 168, 174, 176, 180, 182, 183

Offset: 1

Timothy L. Tiffin, Jul 06 2016

nonn

Numbers which appear in A000593.

Possible values for the sum of odd divisors of the positive integers, in increasing order. - Omar E. Pol, Jul 06 2016

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000593, subsequence of A002191, A274793 (complement).

N:= 10000:# to get all terms <= N
p:= 3:
S:= {1}:
while p < N do
  S:= map(s -> seq(s*(p^(e+1)-1)/(p-1), e=0..ilog[p](1+N*(p-1)/s)-1), S);
  p:= nextprime(p);
od:
sort(convert(S,list)); # Robert Israel, Jul 06 2016

Union@ Table[Total@ Select[Divisors@ n, OddQ], {n, 200}] (* Michael De Vlieger, Jul 07 2016 *)

list(lim)=lim\=1; my(v=[1]); forprime(p=3,lim\4, my(t,u=v,lm); for(e=1,logint(lim,p), t=(p^(e+1)-1)/(p-1); lm=lim\t; u=concat(u,select(k->k<=lm,v)*t)); v=Set(u)); Set(concat(v, apply(p->p+1, primes([lim\4,lim-1])))) \\ Charles R Greathouse IV, Jul 06 2016

A291109 Numbers that are not the sum of the squarefree divisors of some natural number.

Original entry on oeis.org

2, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 111

Offset: 1

Ilya Gutkovskiy, Aug 17 2017

nonn

Impossible values for A048250 (numbers k in increasing order such that A048250(m) = k has no solution).
Numbers that are not of the form Product (p_i + 1), p is a prime, so all odd numbers (except 1 and 3) are in this sequence.
Also numbers that are not the sum of the divisors of some squarefree number.

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of divisors

Cf. A005114, A005117, A007369, A048250, A048995, A062822, A063948, A064000, A203444, A206778, A274793.

sort(convert({$1..1000} minus map(numtheory:-sigma, select(numtheory:-issqrfree, {$1..1000})),list)); # Robert Israel, Jun 26 2018

TakeWhile[Complement[Range@ #, Union@ Table[Total@ Select[Divisors@ n, SquareFreeQ], {n, 2 #}]], Function[k, k <= #]] &@ 111

cp's OEIS Frontend

A274790 Numbers in the range of the sum of odd divisors function.

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