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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
1, 510, 11235, 12243, 14223, 136374, 142494, 145266, 148614, 163158, 171465, 181815, 214863, 240963, 246507, 323976, 397182, 404994, 1548798 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)