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A256635 a(n) = the smallest number k such that the base-10 digital sum of sigma(k) is n.

%I A256635 #34 Jun 06 2025 12:14:07
%S A256635 1,19,2,3,13,5,4,7,10,12,28,18,192,67,42,273,52,138,324,336,196,300,
%T A256635 372,438,2716,997,1590,3468,2512,3260,5817,5692,4112,17472,10852,
%U A256635 15840,18496,27252,22860,24300,31572,35172,61488,165652,138438,265252,285652,292860
%N A256635 a(n) = the smallest number k such that the base-10 digital sum of sigma(k) is n.
%C A256635 a(n) = the smallest number k such that A007953(A000203(k)) = n.
%C A256635 Note that A007953(A000203(k)) is also A067342(k).
%H A256635 Max Alekseyev, <a href="/A256635/b256635.txt">Table of n, a(n) for n = 1..100</a> (terms for n = 1..66 from Chai Wah Wu)
%e A256635 For n = 5; digital sum of sigma(13) = digital sum of 14 = 5. The number 13 is the smallest number with this property so a(5) = 13.
%p A256635 N := 10^6: # return all values before the first > N
%p A256635 for n from 1 to N do
%p A256635    v:= convert(convert(numtheory:-sigma(n),base,10),`+`);
%p A256635    if not assigned(A[v]) then A[v]:= n fi;
%p A256635 od:
%p A256635 for count from 1 while assigned(A[count]) do od:
%p A256635 seq(A[i],i=1..count-1); # _Robert Israel_, Apr 09 2015
%t A256635 f[n_] := Block[{k = 1}, While[Plus @@ IntegerDigits[DivisorSigma[1, k]] != n, k++]; k]; Array[f, 48] (* _Michael De Vlieger_, Apr 07 2015 *)
%o A256635 (Magma) A256635:=func<n|exists(r){k:k in[1..10000000] | &+Intseq(SumOfDivisors(k)) eq n }select r else 0>; [A256635(n):n in[1..50]];
%o A256635 (PARI) a(n) = {my(k = 1); while(sumdigits(sigma(k)) != n, k++); k;} \\ _Michel Marcus_, Apr 09 2015
%o A256635 (Python)
%o A256635 from sympy.ntheory.factor_ import divisor_sigma
%o A256635 def A256635(n):
%o A256635     k = 1
%o A256635     while sum(int(d) for d in str(divisor_sigma(k))) != n:
%o A256635         k += 1
%o A256635     return k # _Chai Wah Wu_, Apr 18 2015
%Y A256635 Cf. A000203, A007953, A067342, A256642.
%K A256635 nonn,base
%O A256635 1,2
%A A256635 _Jaroslav Krizek_, Apr 06 2015