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A331036
Odd values of the sum-of-divisors function sigma (A000203), listed by increasing size and with multiplicity.
2
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 08 2020
STATUS
approved