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.

A202147 Numbers k such that the sum of digits^4 of k equals Sum_{d|k, 1

Original entry on oeis.org

1005, 5405, 89195, 92029, 107707, 149851, 323723, 524371, 610171, 999643, 1119253, 1134227, 1728787, 1900523, 2045171, 2170451, 2668381, 3351833, 3361717, 3611227, 5364059, 6571483, 7710883, 7865659, 8938691, 9286331, 9362051, 9593833, 10841387, 11507813
Offset: 1

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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 fourth powers of the digits of n is at most 9^4*log_10(n+1). Last term is a(101) = 163998389. - Giovanni Resta, Oct 05 2018

Examples

			1005 is in the sequence because 1^4 + 0^4 + 0^4 + 5^4 = 626, and the sum of the divisors 1< d<1005 is  3 + 5 +15 + 67 + 201+ 335 = 626.
		

Crossrefs

Programs

  • Mathematica
    Q[n_]:=Module[{a=Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^4]]; Select[Range[2, 10^7], Q]

Extensions

Keywords fini and full added by Giovanni Resta, Oct 05 2018

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.