4 ms·
Its sum of divisors is 385735449676045680000, very close to the original number. In base ten that shares the first five digits with the number itself. It's also
by Y_Y 4y ago
Its sum of divisors is 385735449676045680000, very close to the original number. In base ten that shares the first five digits with the number itself. It's also small since the expected value is the number itself times π²/6, whereas our sum of divisors is slightly less than the original number. This is probably due to its only having three prime factors, all multiplicity 1. That's unusual too but estimating what we would expect is awkward.
edit: I should add that all of this was well known to Ramanujan, with whom I share a birthday. He famously was able to refute the uninterestingness of 1729.
- joshuaissac 4y agoHow did you figure out all of that? Surely, you don't mean that Ramanujan knew about 385734874675783289473 because the sibling comment shows that it was keyboard-smashed.
- Y_Y 4y agoWhatever the number theory equivalent of keyboard mashing is. I just checked a few typical functions and that one seemed interesting. Ramanujan wrote his thesis (equivalent) on highly composite numbers and studied things like the "divisor functions" related to summing (powers of) a number's divisors. I'd almost be ready to say he wouldn't have had anything to say about Lacker's Number, but then he was responsible for quite a few results which he had no reasonable way of knowing, given the knowledge available.