A256635 - OEIS

%I #28 Feb 19 2024 09:57:56

%S 1,19,2,3,13,5,4,7,10,12,28,18,192,67,42,273,52,138,324,336,196,300,

%T 372,438,2716,997,1590,3468,2512,3260,5817,5692,4112,17472,10852,

%U 15840,18496,27252,22860,24300,31572,35172,61488,165652,138438,265252,285652,292860

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

%C a(n) = the smallest number k such that A007953(A000203(k)) = n.

%C Note that A007953(A000203(k)) is also A067342(k).

%H 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 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 N := 10^6: # return all values before the first > N

%p for n from 1 to N do

%p    v:= convert(convert(numtheory:-sigma(n),base,10),`+`);

%p    if not assigned(A[v]) then A[v]:= n fi;

%p od:

%p for count from 1 while assigned(A[count]) do od:

%p seq(A[i],i=1..count-1); # _Robert Israel_, Apr 09 2015

%t f[n_] := Block[{k = 1}, While[Plus @@ IntegerDigits[DivisorSigma[1, k]] != n, k++]; k]; Array[f, 48] (* _Michael De Vlieger_, Apr 07 2015 *)

%o (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 (PARI) a(n) = {my(k = 1); while(sumdigits(sigma(k)) != n, k++); k;} \\ _Michel Marcus_, Apr 09 2015

%o (Python)

%o from sympy.ntheory.factor_ import divisor_sigma

%o def A256635(n):

%o ....k = 1

%o ....while sum(int(d) for d in str(divisor_sigma(k))) != n:

%o ........k += 1

%o ....return k # _Chai Wah Wu_, Apr 18 2015

%Y Cf. A000203, A007953, A067342, A256642.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Apr 06 2015