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Revision History for A369259 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

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Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.
(history; published version)
#9 by OEIS Server at Thu Jan 25 15:29:00 EST 2024
LINKS

Antti Karttunen, <a href="/A369259/b369259_1.txt">Table of n, a(n) for n = 1..65537</a>

#8 by Michael De Vlieger at Thu Jan 25 15:29:00 EST 2024
STATUS

proposed

approved

Discussion
Thu Jan 25
15:29
OEIS Server: Installed first b-file as b369259.txt.
#7 by Antti Karttunen at Thu Jan 25 13:24:45 EST 2024
STATUS

editing

proposed

#6 by Antti Karttunen at Thu Jan 25 13:24:19 EST 2024
COMMENTS

a(i) = a(j) => A323368(i) = A323368(j) => A291751(i) = A291751(j) => A286603(i) = A286603(j),,

a(i) = a(j) => A369260(i) = A369260(j) => A286603(i) = A286603(j),.

a(i) = a(j) => A323368(i) = A323368(j) [Conjectured].

STATUS

proposed

editing

#5 by Antti Karttunen at Thu Jan 25 13:14:29 EST 2024
STATUS

editing

proposed

#4 by Antti Karttunen at Thu Jan 25 13:08:10 EST 2024
NAME

Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.

#3 by Antti Karttunen at Thu Jan 25 13:07:40 EST 2024
LINKS

Antti Karttunen, <a href="/A369259/b369259_1.txt">Table of n, a(n) for n = 1..65537</a>

<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

<a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

#2 by Antti Karttunen at Thu Jan 25 13:03:36 EST 2024
NAME

allocated Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for Antti Karttunenall i, j >= 1.

DATA

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 23, 24, 25, 26, 27, 28, 29, 21, 30, 31, 32, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 29, 31, 43, 44, 45, 46, 47, 48, 49, 46, 50, 51, 52, 53, 54, 55, 39, 56, 57, 58, 59, 60, 61, 62, 59, 46, 63, 64, 65, 66, 67, 62, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 59

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the triplet [A003557(j), A048250(i), A342671(n)].

For all i, j >= 1:

a(i) = a(j) => A291751(i) = A291751(j) => A286603(i) = A286603(j),

a(i) = a(j) => A369260(i) = A369260(j) => A286603(i) = A286603(j),

a(i) = a(j) => A323368(i) = A323368(j) [Conjectured].

PROG

(PARI)

up_to = 65537;

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; };

A003557(n) = (n/factorback(factor(n)[, 1]));

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

A342671(n) = gcd(sigma(n), A003961(n));

Aux369259(n) = [A003557(n), A048250(n), A342671(n)];

v369259 = rgs_transform(vector(up_to, n, Aux369259(n)));

A369259(n) = v369259[n];

CROSSREFS

Cf. A000203, A003557, A003961, A048250, A286603, A291751, A369260.

Differs from related A296089 and A323368 for the first time at n=79, where a(79) = 69, while A296089(79) = A323368(79) = 51.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jan 25 2024

STATUS

approved

editing

#1 by Antti Karttunen at Thu Jan 18 03:58:45 EST 2024
NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved