OFFSET
1,1
COMMENTS
This is a subsequence of A156942, "odd abundant numbers whose abundance is odd". Proof: If sigma(k) > 2*k, and sigma(k) were even, then sigma(k)/2 would be an integer and a divisor of sigma(k), and we could compute A003415(sigma(k)) as A003415(2)*(sigma(k)/2) + 2*A003415(sigma(k)/2) by the definition of the arithmetic derivative. But that value is certainly larger than k, because sigma(k)/2 > k, therefore sigma(k) must be an odd number, with also its abundance sigma(k)-(2k) odd. This also entails that all terms are squares. See A347891 for the square roots.
The first term that is not a multiple of 25 is a(146) = 6800806089 = 82467^2.
This is not a subsequence of A325311. The first term that is not present there is a(5) = 3080025.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 19 2021
STATUS
approved