A331036 Odd values of the sum-of-divisors function sigma (A000203), listed by increasing size and with multiplicity.

1, 3, 7, 13, 15, 31, 31, 39, 57, 63, 91, 93, 121, 127, 133, 171, 183, 195, 217, 255, 307, 363, 381, 399, 399, 403, 403, 465, 511, 549, 553, 741, 781, 819, 847, 855, 871, 921, 931, 961, 993, 1023, 1093, 1143, 1209, 1281, 1407, 1651, 1659, 1723, 1729, 1767, 1767, 1815, 1893, 1953

Offset: 1

Author

M. F. Hasler, Jan 08 2020

Keywords

• nonn

Comments

See A060657 for the range (without repeated terms) and A152677 for the subsequence of odd values in A000203.

Links

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

Crossrefs

Cf. A060657, A023195 (subset of primes), A152677 (subsequence of odd values in A000203), A300869 (repeated terms).

Programs

Maple

N:= 2000: # for terms <= N
Res:= NULL:
for m from 1 to floor(sqrt(N)) by 2 do
  sm:= numtheory:-sigma(m^2);
  for k from 1 to floor(log[2](N/sm+1)) do
    v:= sm*(2^k-1);
    if v <= N then Res:= Res, v; count:= count+1 fi;
  od
od:
sort([Res]); # Robert Israel, Jan 14 2020

Mathematica

Sort@ Select[DivisorSigma[1, Range@ 2000], OddQ[#] && # < 2000 &] (* Giovanni Resta, Jan 08 2020 *)

PARI

list(lim)=select(k->k<=lim, vecsort(apply(sigma, concat(vector(sqrtint(lim\1), i, i^2), vector(sqrtint(lim\2), i, 2*i^2))))) \\ Charles R Greathouse IV, Feb 15 2013 [originally added in A152677]