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

1,2

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

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 *)

Prog

(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]

Crossrefs

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

Sequence in context: A164344 A002254 A356211 * A060657 A192148 A151875

Adjacent sequences: A331033 A331034 A331035 * A331037 A331038 A331039

Keyword

nonn

Author

M. F. Hasler, Jan 08 2020

Status

approved