The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A322024 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A322024

Lexicographically earliest such sequence a that a(i) = a(j) => A014197(i) = A014197(j) and A081373(i) = A081373(j), for all i, j. Here A081373(n) gives the number of k, 1 <= k <= n, with phi(k) = phi(n), while A014197(n) gives the number of integers m with phi(m) = n.
(history; published version)

#6 by Susanna Cuyler at Sun Dec 02 20:53:34 EST 2018

STATUS

proposed

approved

#5 by Antti Karttunen at Sat Dec 01 16:39:21 EST 2018

STATUS

editing

proposed

#4 by Antti Karttunen at Thu Nov 29 11:19:27 EST 2018

NAME

Lexicographically earliest such sequence a that a(i) = a(j) => A014197(i) = A014197(j) and A081373(i) = A081373(j), for all i, j. Here A081373 is (n) gives the ordinal transforms number of Euler k, 1 <= k <= n, with phi(k) = phi, and (n), while A014197 is (n) gives the number of integers m with phi(m) = n.

Discussion

Thu Nov 29

11:23

Antti Karttunen: Used as a filtering sequence, thus longer b-file and the data-section, please do not shorten, thanks!

#3 by Antti Karttunen at Thu Nov 29 11:13:18 EST 2018

LINKS

Antti Karttunen, <a href="/A322024/b322024.txt">Table of n, a(n) for n = 1..65537</a>

#2 by Antti Karttunen at Thu Nov 29 11:09:15 EST 2018

NAME

allocated Lexicographically earliest such sequence a that a(i) = a(j) => A014197(i) = A014197(j) and A081373(i) = A081373(j), for Antti Karttunenall i, j. Here A081373 is the ordinal transforms of Euler phi, and A014197 is the number of integers m with phi(m) = n.

DATA

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 7, 14, 3, 15, 3, 10, 7, 16, 3, 17, 3, 18, 7, 10, 3, 19, 3, 10, 7, 20, 3, 21, 3, 22, 10, 14, 3, 23, 7, 24, 3, 16, 3, 16, 7, 25, 7, 14, 3, 26, 3, 7, 10, 27, 3, 17, 3, 10, 3, 28, 3, 29, 3, 24, 10, 30, 7, 31, 3, 15, 3, 16, 3, 32, 3, 10, 3, 33, 3, 34, 7, 2, 10, 7, 10, 35, 3, 24, 24, 21, 3, 28, 3, 2, 10

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A014197(n), A081373(n)].

PROG

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197

v081373 = ordinal_transform(vector(up_to, n, eulerphi(n)));

A081373(n) = v081373[n];

v322024 = rgs_transform(vector(up_to, n, [A014197(n), A081373(n)]));

A322024(n) = v322024[n];

CROSSREFS

Cf. A014197, A081373, A305896, A319339, A322023.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Nov 29 2018

STATUS

approved

editing

#1 by Antti Karttunen at Sat Nov 24 11:01:25 EST 2018

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved