OFFSET
1,1
COMMENTS
Every term has an odd number of prime divisors (A001221(k) is odd), since if not, sopfr(k) would be even, and so not divide k, which is odd.
Some Carmichael numbers appear in this sequence, the first of which is 3240392401.
From Robert Israel, Jul 05 2019: (Start)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
105=3*5*7; sum of prime factors = 15 and 105 = 7*15, so 105 is a term.
MAPLE
with(NumberTheory);
N := 500;
for n from 2 to N do
S := PrimeFactors(n);
X := add(S);
if IsSquareFree(n) and not mod(n, 2) = 0 and not isprime(n) and mod(n, X) = 0 then print(n);
end if:
end do:
MATHEMATICA
aQ[n_] := Module[{f = FactorInteger[n]}, p=f[[;; , 1]]; e=f[[;; , 2]]; Length[e] > 1 && Max[e]==1 && Divisible[n, Plus@@(p^e)]]; Select[Range[1, 61000, 2], aQ] (* Amiram Eldar, Jul 04 2019 *)
PROG
(Magma) [k:k in [2*d+1: d in [1..35000]]|IsSquarefree(k) and not IsPrime(k) and k mod &+PrimeDivisors(k) eq 0]; // Marius A. Burtea, Jun 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
David James Sycamore, Jun 13 2019
STATUS
approved