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

Author

Michael Savoric, Aug 05 2015

Keywords

• nonn
• base
• fini
• full
• less

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

Examples

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

Crossrefs

Cf. A000203, A000583, A007953, A055013.

Programs

Magma

[n: n in [1..3*10^6] | DivisorSigma(1,n) eq (&+Intseq(n)^4)]; // Vincenzo Librandi, Aug 29 2015

Mathematica

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

PARI

isok(n) = sigma(n) == sumdigits(n)^4; \\ Michel Marcus, Aug 06 2015

Formula

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