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

Author

Timothy L. Tiffin, Jul 06 2016

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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