cp's OEIS Frontend

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

%I A260598 #46 Sep 08 2022 08:46:13
%S A260598 1,510,11235,12243,14223,136374,142494,145266,148614,163158,171465,
%T A260598 181815,214863,240963,246507,323976,397182,404994,1548798
%N A260598 Numbers n such that the sum of the divisors of n equals the fourth power of the sum of the digits of n.
%C A260598 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
%F A260598 A000583(A007953(a(n))) = A000203(a(n)).
%e A260598 510 is in the sequence, since (1 + 2 + 3 + 5 + ... + 255 + 510) = (5 + 1 + 0)^4.
%t A260598 n = 10000000;
%t A260598 list = {};
%t A260598 x = 1;
%t A260598 While[x <= n,
%t A260598   If[Total[Divisors[x]] == Total[IntegerDigits[x]]^4,
%t A260598    AppendTo[list, x]];
%t A260598   x = x + 1
%t A260598   ];
%t A260598 list
%o A260598 (PARI) isok(n) = sigma(n) == sumdigits(n)^4; \\ _Michel Marcus_, Aug 06 2015
%o A260598 (Magma) [n: n in [1..3*10^6] | DivisorSigma(1,n) eq (&+Intseq(n)^4)]; // _Vincenzo Librandi_, Aug 29 2015
%Y A260598 Cf. A000203, A000583, A007953, A055013.
%K A260598 nonn,base,fini,full,less
%O A260598 1,2
%A A260598 _Michael Savoric_, Aug 05 2015