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A202279 Numbers n such that the sum of digits^3 of n equals the sum of d|n, 1<d<n. 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

Table of n, a(n) for n=1..18.

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

Cf. A070308, A202279, A202147, A202285, A202240.

Sequence in context: A172836 A087001 A025379 * A035702 A172335 A217531

Adjacent sequences:  A202276 A202277 A202278 * A202280 A202281 A202282

KEYWORD

nonn,base,fini,full

AUTHOR

Michel Lagneau, Dec 15 2011

STATUS

approved

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Last modified October 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)