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Jul 10 at 17:07 comment added Max Alekseyev @Notamathematician: I've reworked the iterated sum expression. Unfortunately, it does not look as easy as I originally hoped for, and there is no apparent explicit formula.
Jul 10 at 17:06 history edited Max Alekseyev CC BY-SA 4.0
re-worked; added 1 character in body; added 13 characters in body
Jul 10 at 1:59 comment added Notamathematician Unfortunately, the formula is still far from the true one. Please check the result in some program.
Jul 9 at 22:38 history edited Max Alekseyev CC BY-SA 4.0
formula corrected
Jul 9 at 18:05 comment added Notamathematician Thank you very much for answer! Could you please double check your final formula? As for my conjectured formula, I tested it separately for the first few $p$ without counterexamples. I would be very grateful if you could give me a working closed form for $a(n)$.
Jul 9 at 17:34 vote accept Notamathematician
Jul 9 at 15:12 history answered Max Alekseyev CC BY-SA 4.0