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

%I A331036 #16 Jan 15 2020 00:24:35
%S A331036 1,3,7,13,15,31,31,39,57,63,91,93,121,127,133,171,183,195,217,255,307,
%T A331036 363,381,399,399,403,403,465,511,549,553,741,781,819,847,855,871,921,
%U A331036 931,961,993,1023,1093,1143,1209,1281,1407,1651,1659,1723,1729,1767,1767,1815,1893,1953
%N A331036 Odd values of the sum-of-divisors function sigma (A000203), listed by increasing size and with multiplicity.
%C A331036 See A060657 for the range (without repeated terms) and A152677 for the subsequence of odd values in A000203.
%H A331036 Robert Israel, <a href="/A331036/b331036.txt">Table of n, a(n) for n = 1..10000</a>
%p A331036 N:= 2000: # for terms <= N
%p A331036 Res:= NULL:
%p A331036 for m from 1 to floor(sqrt(N)) by 2 do
%p A331036   sm:= numtheory:-sigma(m^2);
%p A331036   for k from 1 to floor(log[2](N/sm+1)) do
%p A331036     v:= sm*(2^k-1);
%p A331036     if v <= N then Res:= Res, v; count:= count+1 fi;
%p A331036   od
%p A331036 od:
%p A331036 sort([Res]); # _Robert Israel_, Jan 14 2020
%t A331036 Sort@ Select[DivisorSigma[1, Range@ 2000], OddQ[#] && # < 2000 &] (* _Giovanni Resta_, Jan 08 2020 *)
%o A331036 (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]
%Y A331036 Cf. A060657, A023195 (subset of primes), A152677 (subsequence of odd values in A000203), A300869 (repeated terms).
%K A331036 nonn
%O A331036 1,2
%A A331036 _M. F. Hasler_, Jan 08 2020