The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A325130 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A325130

Numbers in whose prime factorization the exponent of prime(k) is not equal to k for any prime index k.
(history; published version)

#19 by Joerg Arndt at Sat Jan 09 04:48:19 EST 2021

STATUS

reviewed

approved

#18 by Michel Marcus at Sat Jan 09 03:43:33 EST 2021

STATUS

proposed

reviewed

#17 by Amiram Eldar at Sat Jan 09 03:22:35 EST 2021

STATUS

editing

proposed

#16 by Amiram Eldar at Sat Jan 09 03:22:28 EST 2021

CROSSREFS

Cf. Complement of A276936.

STATUS

proposed

editing

#15 by Amiram Eldar at Sat Jan 09 03:16:00 EST 2021

STATUS

editing

proposed

#14 by Amiram Eldar at Sat Jan 09 02:56:37 EST 2021

COMMENTS

The asymptotic density of this sequence is Product_{k>=1} (1 - 1/prime(k)^k + 1/prime(k)^(k+1)) = 0.68974964705635552968... - Amiram Eldar, Jan 09 2021

#13 by Amiram Eldar at Sat Jan 09 02:56:05 EST 2021

NAME

Numbers n in whose prime factorization the exponent of prime(k) is not equal to k for any prime index k.

STATUS

approved

editing

#12 by Alois P. Heinz at Mon Oct 28 11:53:49 EDT 2019

STATUS

editing

approved

#11 by Alois P. Heinz at Mon Oct 28 11:53:46 EDT 2019

LINKS

Alois P. Heinz, <a href="/A325130/b325130.txt">Table of n, a(n) for n = 1..10000</a>

#10 by Alois P. Heinz at Mon Oct 28 11:49:23 EDT 2019

MAPLE

q:= n-> andmap(i-> numtheory[pi](i[1])<>i[2], ifactors(n)[2]):

a:= proc(n) option remember; local k; for k from 1+

`if`(n=1, 0, a(n-1)) while not q(k) do od; k

end:

seq(a(n), n=1..80); # Alois P. Heinz, Oct 28 2019

STATUS

approved

editing