OFFSET
1,1
COMMENTS
Conjecture: a(n) is of the form a(n) = 2^i*p^j with i, j integers and p prime. This has been verified for n up to 10^7.
Observation: For n < = 10^7, p belongs to the set E = {13, 37, 61, 73, 109, 157, 181, 193, 229, 277, 313, 373, 397, 409, 421, 433, 457, 541, 601, 613, 661, 673, 709, 733, 757, 769, 829, 853, 877, 997, 1009, 1021, 1033, 1069, 1093, 1117, 1129, 1153, 1201, 1213, 1237, 1297, 1381, 1429, 1453, 1489}. We observe that E minus {181, 433, 601, 769, 853, 1021, 1429} belongs to A082539.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
MATHEMATICA
lst={}; Do[If[SquareFreeQ[Total[Select[Divisors[n], SquareFreeQ]]]&& SquareFreeQ[DivisorSigma[1, n]-Total[Select[Divisors[n], SquareFreeQ]]], AppendTo[lst, n]], {n, 300000}]; lst
PROG
(PARI) isok(n) = my(sd = sumdiv(n, d, d*issquarefree(d))); issquarefree(sd) && issquarefree(sigma(n) - sd); \\ Michel Marcus, Mar 17 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 17 2018
STATUS
approved