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

1, 19, 2, 3, 13, 5, 4, 7, 10, 12, 28, 18, 192, 67, 42, 273, 52, 138, 324, 336, 196, 300, 372, 438, 2716, 997, 1590, 3468, 2512, 3260, 5817, 5692, 4112, 17472, 10852, 15840, 18496, 27252, 22860, 24300, 31572, 35172, 61488, 165652, 138438, 265252, 285652, 292860

Offset

1,2

Comments

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

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

Links

Max Alekseyev, Table of n, a(n) for n = 1..100 (terms for n = 1..66 from Chai Wah Wu)

Example

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.

Maple

N := 10^6: # return all values before the first > N
for n from 1 to N do
   v:= convert(convert(numtheory:-sigma(n), base, 10), `+`);
   if not assigned(A[v]) then A[v]:= n fi;
od:
for count from 1 while assigned(A[count]) do od:
seq(A[i], i=1..count-1); # Robert Israel, Apr 09 2015

Mathematica

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

Prog

(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]]
(PARI) a(n) = {my(k = 1); while(sumdigits(sigma(k)) != n, k++); k; } \\ Michel Marcus, Apr 09 2015
(Python)
from sympy.ntheory.factor_ import divisor_sigma
def A256635(n):
....k = 1
....while sum(int(d) for d in str(divisor_sigma(k))) != n:
........k += 1
....return k # Chai Wah Wu, Apr 18 2015

Crossrefs

Cf. A000203, A007953, A067342, A256642.

Sequence in context: A040357 A040358 A051312 * A040359 A040360 A040351

Adjacent sequences: A256632 A256633 A256634 * A256636 A256637 A256638

Keyword

nonn,base

Author

Jaroslav Krizek, Apr 06 2015

Status

approved