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.
%I A097464 #15 Oct 24 2024 09:26:01
%S A097464 6,28,496,47520,288288,308474880
%N A097464 5-infinitary perfect numbers: numbers k such that 5-infinitary-sigma(k) = 2*k.
%C A097464 Here 5-infinitary-sigma(k) means sum of 5-infinitary-divisors of k. If k = Product p_i^r_i and d = Product p_i^s_i, each s_i has a digit a <= b in its 5-ary expansion everywhere that the corresponding r_i has a digit b, then d is a 5-infinitary-divisor of k.
%C A097464 Is it certain that 308474880 is the 6th term? _M. F. Hasler_, Nov 20 2010
%C A097464 Data is verified. a(7) > 10^11, if it exists. - _Amiram Eldar_, Oct 24 2024
%F A097464 {k: A097863(k) = 2*k}.
%e A097464 Factorizations: 2*3, 2^2*7, 2^4*31, 2^5*3^3*5*11, 2^5*3^2*7*11*13, 2^10*3*5*7*19*151.
%t A097464 f[p_, e_] := Module[{d = IntegerDigits[e, 5]}, m = Length[d]; Product[(p^((d[[j]] + 1)*5^(m - j)) - 1)/(p^(5^(m - j)) - 1), {j, 1, m}]]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[300000], s[#] == 2*# &] (* _Amiram Eldar_, Oct 24 2024 *)
%Y A097464 Cf. A007357, A038182, A074849, A097863.
%K A097464 nonn,more
%O A097464 1,1
%A A097464 _Yasutoshi Kohmoto_
%E A097464 Missing a(4) inserted by _R. J. Mathar_, Nov 20 2010