OFFSET
1,2
COMMENTS
Ratio r(n) = a(n)/A336839(n) is multiplicative. For example r(3) = 3/1, r(4) = 13/3, thus r(12) = r(3)*r(4) = 13/1.
Conjecture: For all primes p with an odd exponent e, a(p^e) is a multiple of A048673(p). Note that q+1 is a divisor of (q+1)^e - sigma(q^e) = (q+1)^e - (1 + q + q^2 + ... + q^e) when e is odd, thus also A048673(p) = (q+1)/2 is, where q = A003961(p), thus the conjecture holds, unless the denominator (A336839) has enough prime factors of A048673(p).
LINKS
FORMULA
PROG
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Aug 07 2020
STATUS
approved