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Revision History for A099308

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Showing entries 1-10 | older changes

A099308

Numbers m whose k-th arithmetic derivative is zero for some k. Complement of A099309.
(history; published version)

#31 by Michael De Vlieger at Fri Jan 06 15:23:42 EST 2023

STATUS

proposed

approved

#30 by Antti Karttunen at Fri Jan 06 14:50:54 EST 2023

STATUS

editing

proposed

#29 by Antti Karttunen at Fri Jan 06 03:23:49 EST 2023

CROSSREFS

Cf. A276086, A328116, A351255, (permutation of nonzero terms), A351257, A351259, A351261, A351072 (number of prime(k)-smooth terms > 1).

#28 by Antti Karttunen at Fri Jan 06 03:19:27 EST 2023

PROG

\\ The following program would get stuck in nontrivial loops. However, we assume that the conjecture 3 in Ufnarovski & Åhlander paper holds ("The differential equation n ^(k) = n has only trivial solutions p^p for primes p").

CROSSREFS

Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099309 (complement, numbers whose k-th arithmetic derivative is nonzero for all k), A351078 (first noncomposite reached when iterating the derivative from these numbers), A351079 (the largest term on such paths).

Cf. also A256750, (number of iterations needed to reach either 0 or a number with a factor of the form p^p), A327969, A351088.

#27 by Antti Karttunen at Fri Jan 06 03:15:08 EST 2023

REFERENCES

See A003415.

PROG

\\ The following program would get stuck in nontrivial loops. However, we assume that the conjecture 3 in Ufnarovski & Åhlander paper holds ("The differential equation n (k) = n has only trivial solutions p ^p for primes p").

#26 by Antti Karttunen at Fri Jan 06 03:13:24 EST 2023

CROSSREFS

Union of A359544 and A359545.

STATUS

approved

editing

#25 by Michael De Vlieger at Mon Feb 14 11:20:45 EST 2022

STATUS

proposed

approved

#24 by Antti Karttunen at Mon Feb 14 08:30:01 EST 2022

STATUS

editing

proposed

#23 by Antti Karttunen at Mon Feb 14 08:29:53 EST 2022

CROSSREFS

Cf. A276086, A328116, A351255, A351257, A351259, A351261, A351072 (number of prime(k)-smooth terms > 01).

STATUS

proposed

editing

#22 by Michel Marcus at Mon Feb 14 08:20:05 EST 2022

STATUS

editing

proposed

Discussion

Mon Feb 14

08:29

Antti Karttunen: Why is that "m" needed as it is not referred later in the definition?