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A202279 Numbers k such that the sum of digits^3 of k equals Sum_{d|k, 1<d<k} d. 4
142, 160, 1375, 6127, 12643, 51703, 86833, 103039, 104647, 112093, 137317, 218269, 261883, 266923, 449881, 505891, 617569, 907873 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The sequence is finite because the restricted sum of divisors of n, for n composite, is at least sqrt(n), while the sum of the cubes of the digits of n is at most 9^3*log_10(n+1). - Giovanni Resta, Oct 05 2018
LINKS
FORMULA
{n: A055012(n) = A048050(n)}. - R. J. Mathar, Dec 15 2011
EXAMPLE
160 is in the sequence because 1^3 + 6^3 + 0^3 = 217, and the sum of the divisors 1< d<160 is 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 80 = 217.
MAPLE
A055012 := proc(n)
add(d^3, d=convert(n, base, 10)) ;
end proc:
A048050 := proc(n)
if n > 1 then
numtheory[sigma](n)-1-n ;
else
0;
end if;
end proc:
isA202279 := proc(n)
A055012(n) = A048050(n) ;
end proc:
for n from 1 do
if isA202279(n) then
printf("%d, \n", n);
end if;
end do; # R. J. Mathar, Dec 15 2011
MATHEMATICA
Q[n_]:=Module[{a=Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^3]]; Select[Range[2, 5*10^7], Q]
Select[Range[1000000], DivisorSigma[1, #]-#-1==Total[IntegerDigits[#]^3]&] (* Harvey P. Dale, Jul 19 2014 *)
CROSSREFS
Sequence in context: A172836 A087001 A025379 * A035702 A172335 A217531
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Dec 15 2011
STATUS
approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)