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 A346556 #8 Mar 18 2022 00:28:35
%S A346556 1,3,16,48,336,14448,376464,17716019376,419963172816
%N A346556 8-Sondow numbers: numbers k such that p^s divides k/p + 8 for every prime power divisor p^s of k.
%C A346556 Numbers k such that A235137(k) == 8 (mod k).
%C A346556 A positive integer k is a 8-Sondow number if satisfies any of the following equivalent properties:
%C A346556 1) p^s divides k/p + 8 for every prime power divisor p^s of k.
%C A346556 2) 8/k + Sum_{prime p|k} 1/p is an integer.
%C A346556 3) 8 + Sum_{prime p|k} k/p == 0 (mod k).
%C A346556 4) Sum_{i=1..k} i^phi(k) == 8 (mod k).
%C A346556 Other numbers in the sequence: 17716019376, 419963172816, 67923372668477507285654170088688
%H A346556 Github, <a href="https://jonathansondow.github.io/">Jonathan Sondow (1943 - 2020)</a>
%H A346556 J. M. Grau, A. M. Oller-Marcén and D. Sadornil, <a href="https://arxiv.org/abs/2111.14211">On µ-Sondow Numbers</a>, arXiv:2111.14211 [math.NT], 2021.
%H A346556 J. M. Grau, A. M. Oller-Marcen and J. Sondow, <a href="https://arxiv.org/abs/1309.7941">On the congruence 1^n + 2^n + ... + n^n = d (mod n), where d divides n</a>, arXiv:1309.7941 [math.NT], 2013-2014.
%t A346556 Sondow[mu_][n_]:=Sondow[mu][n]=Module[{fa=FactorInteger[n]},IntegerQ[mu/n+Sum[1/fa[[i,1]],{i,Length[fa]}]]]
%t A346556 Select[Range[400000],Sondow[8][#]&]
%Y A346556 Cf. A054377, A007850, A235137, A348058, A348059.
%Y A346556 (-1) and (-2) -Sondow numbers: A326715, A330069.
%Y A346556 1-Sondow to 9-Sondow numbers: A349193, A330068, A346551, A346552, A346553, A346554, A346555, this sequence, A346557.
%K A346556 nonn,more
%O A346556 1,2
%A A346556 _José María Grau Ribas_, Feb 04 2022
%E A346556 a(8)-a(9) verified by _Martin Ehrenstein_, Feb 04 2022