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#22 by Jon E. Schoenfield at Wed Jul 21 00:44:54 EDT 2021
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#21 by Michel Marcus at Wed Jul 21 00:04:23 EDT 2021
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#20 by Jon E. Schoenfield at Tue Jul 20 23:55:43 EDT 2021
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#19 by Jon E. Schoenfield at Tue Jul 20 23:55:16 EDT 2021
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| NAME
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Numbers nk such that A078898(nk) is a power of 2; an analog for A000961 based on factorization-kind of process involving the sieve of Eratosthenes (A083221).
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| COMMENTS
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Numbers nk for which A302041(nk) < 2, or equally, for which A302044(nk) = 1.
Sequence A250245(A000961(nk)) sorted into ascending order, or in other words, numbers nk such that A250246(nk) is a prime power (in A000961).
Numbers nk such that all terms in iteration sequence nk, A302042(nk), A302042(A302042(nk)), A302042(A302042(A302042(nk))), ..., have an equal smallest prime factor (A020639) before the sequence settles to 1, in other words, that they all stay on the same row of A083221. This also forces the column position of each (A078898) to be a power of 2 (A000079).
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| EXAMPLE
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For nk = 21 = 3*7, the smallest prime factor is 3. A302042(21) = 9, and A302042(9) = 3, both (9 and 3) which also have 3 as their smallest prime factor, and after that the sequence settles to 1, as A302042(3) = 1, thus 21 is included in this sequence.
For nk = 27 = 3*3*3, the smallest prime factor is 3. However, A302042(27) = 7, thus 27 is not included in this sequence.
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| STATUS
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approved
editing
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#18 by Susanna Cuyler at Mon Apr 02 21:20:29 EDT 2018
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#17 by Antti Karttunen at Mon Apr 02 16:21:25 EDT 2018
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#16 by Antti Karttunen at Mon Apr 02 16:20:38 EDT 2018
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| COMMENTS
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Numbers n such that all terms in iteration sequence n, A302042(n), A302042(A302042(n)), A302042(A302042(A302042(n))), ..., have an equal smallest prime factor (A020639) before the sequence settles to 1., in other words, that they all stay on the same row of A083221. This also forces the column position of each (A078898) to be a power of 2 (A000079).
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| STATUS
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proposed
editing
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#15 by Antti Karttunen at Mon Apr 02 16:16:13 EDT 2018
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Discussion
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| Mon Apr 02
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| Antti Karttunen: Similarly, after the initial 1, A000961 is all the numbers n such that A246277(n) is a power of 2.
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#14 by Antti Karttunen at Mon Apr 02 16:15:48 EDT 2018
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#13 by Antti Karttunen at Mon Apr 02 15:17:15 EDT 2018
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