cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A202279 Numbers k such that the sum of digits^3 of k equals Sum_{d|k, 1

Original entry on oeis.org

142, 160, 1375, 6127, 12643, 51703, 86833, 103039, 104647, 112093, 137317, 218269, 261883, 266923, 449881, 505891, 617569, 907873
Offset: 1

Views

Author

Michel Lagneau, Dec 15 2011

Keywords

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

Examples

			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.
		

Crossrefs

Programs

  • 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 *)

Formula

{n: A055012(n) = A048050(n)}. - R. J. Mathar, Dec 15 2011

A202285 Numbers k such that the sum of digits^5 of k equals Sum_{d|k, 1

Original entry on oeis.org

118678, 459385, 4150651, 4351003, 15033631, 20402671, 33224707, 35188159, 40460929, 42454261, 50067673, 54610051, 62004127, 77278261, 88720939, 106412347, 113660551, 113852653, 118203559, 121732873, 125252137, 128083639, 162748279, 163869049, 164863987
Offset: 1

Views

Author

Michel Lagneau, Dec 15 2011

Keywords

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 fifth powers of the digits of n is at most 9^5*log_10(n+1). Last term is a(404) = 23184988999. - Giovanni Resta, Oct 05 2018

Examples

			k=118678 is in the sequence because 1^5 + 1^5 + 8^5 + 6^5 + 7^5 + 8^5 = 90121, and the sum of the divisors 1 < d < k =  sigma(k) - k - 1 = 90121.
		

Crossrefs

Programs

  • Mathematica
    Q[n_]:=Module[{a=Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^5]]; Select[Range[2, 10^7], Q]

Extensions

a(11)-a(25) and keywords fini and full added by Giovanni Resta, Oct 05 2018

A202240 a(n) is the smallest number k such that the sum of the n-th powers of the digits of k equals the sum of the divisors of k other than 1 and k.

Original entry on oeis.org

125, 142, 1005, 118678, 706862, 18481615, 122003411, 30330043, 5923078409, 22110133333, 120175787632, 5971473681952
Offset: 2

Views

Author

Michel Lagneau, Dec 16 2011

Keywords

Examples

			a(5) = 118678 because 1^5 + 1^5 + 8^5 + 6^5 + 7^5 + 8^5  = 90121, and sum of the divisors 1 < d < a(5) = sigma(118678) - 118678 - 1 = 90121.
		

Crossrefs

Cf. A070308 (n=2, "Canada perfect numbers").
Cf. A202279 (n=3), A202147 (n=4), A202285 (n=5).

Programs

  • PARI
    f(k, n) = my(d=digits(k)); sum(i=1, #d, d[i]^n);
    a(n) = my(k=1); while(f(k, n) != sigma(k)-k-1, k++); k; \\ Michel Marcus, Sep 29 2018

Extensions

a(8)-a(9) added by Amiram Eldar, Sep 29 2018
a(10)-a(13) from Giovanni Resta, Oct 04 2018
Showing 1-3 of 3 results.