OFFSET
1,2
COMMENTS
Numbers k such that A235137(k) == 3 (mod k).
A positive integer k is a 3-Sondow number if satisfies any of the following equivalent properties:
1) p^s divides k/p + 3 for every prime power divisor p^s of k.
2) 3/k + Sum_{prime p|k} 1/p is an integer.
3) 3 + Sum_{prime p|k} k/p == 0 (mod k).
4) Sum_{i=1..k} i^phi(k) == 3 (mod k).
LINKS
Github, Jonathan Sondow (1943 - 2020)
J. M. Grau, A. M. Oller-Marcén, and D. Sadornil, On µ-Sondow Numbers, arXiv:2111.14211 [math.NT], 2021.
J. M. Grau, A. M. Oller-Marcen and J. Sondow, On the congruence 1^n + 2^n +... + n^n = d (mod n), where d divides n, arXiv:1309.7941 [math.NT], 2013-2014.
MATHEMATICA
Sondow[mu_][n_]:= Sondow[mu][n]= Module[{fa=FactorInteger[n]}, IntegerQ[mu/n+Sum[1/fa[[i, 1]], {i, Length[fa]}]]]
Select[Range[1000000], Sondow[3][#]&]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
José María Grau Ribas, Dec 04 2021
EXTENSIONS
a(8)-a(9) from Martin Ehrenstein, Dec 31 2021
STATUS
approved