A260598 Numbers n such that the sum of the divisors of n equals the fourth power of the sum of the digits of n.

1, 510, 11235, 12243, 14223, 136374, 142494, 145266, 148614, 163158, 171465, 181815, 214863, 240963, 246507, 323976, 397182, 404994, 1548798

Offset

1,2

Comments

Let n be a k-digit number. Then, sigma(n) >= 10^(k-1) and (9*k)^4 >= sum_of_digits(n)^4. So, n must be less than 10^9. - Hiroaki Yamanouchi, Aug 29 2015

Links

Table of n, a(n) for n=1..19.

Formula

A000583(A007953(a(n))) = A000203(a(n)).

Example

510 is in the sequence, since (1 + 2 + 3 + 5 + ... + 255 + 510) = (5 + 1 + 0)^4.

Mathematica

n = 10000000;
list = {};
x = 1;
While[x <= n,
  If[Total[Divisors[x]] == Total[IntegerDigits[x]]^4,
   AppendTo[list, x]];
  x = x + 1
  ];
list

Prog

(PARI) isok(n) = sigma(n) == sumdigits(n)^4; \\ Michel Marcus, Aug 06 2015
(Magma) [n: n in [1..3*10^6] | DivisorSigma(1, n) eq (&+Intseq(n)^4)]; // Vincenzo Librandi, Aug 29 2015

Crossrefs

Cf. A000203, A000583, A007953, A055013.

Sequence in context: A252882 A252883 A196674 * A255179 A144768 A196289

Adjacent sequences: A260595 A260596 A260597 * A260599 A260600 A260601

Keyword

nonn,base,fini,full,less

Author

Michael Savoric, Aug 05 2015

Status

approved