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A322355 Lexicographically earliest such sequence a that a(i) = a(j) => A322351(i) = A322351(j) and A322352(i) = A322352(j), for all i, j. 3
1, 1, 2, 2, 3, 2, 4, 3, 5, 3, 6, 7, 8, 4, 9, 9, 10, 5, 11, 12, 8, 6, 13, 12, 14, 8, 15, 16, 17, 9, 18, 10, 19, 10, 20, 16, 21, 11, 20, 22, 23, 8, 24, 25, 26, 13, 27, 28, 29, 14, 30, 31, 32, 15, 23, 33, 21, 17, 34, 28, 35, 18, 36, 30, 37, 19, 38, 39, 40, 20, 41, 31, 42, 21, 43, 44, 35, 20, 45, 46, 47, 23, 48, 31, 49, 24, 50, 51, 52, 26, 42, 53, 35, 27, 42, 39, 54, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Restricted growth sequence transform of the ordered pair [A322351(n), A322352(n)].

Essentially also the restricted growth sequence transform of the unordered pair {A003557(n), A173557(n)}.

For all i, j:

  A295887(i) = A295887(j) => a(i) = a(j),

  a(i) = a(j) => A322320(i) = A322320(j),

  a(i) = a(j) => A322321(i) = A322321(j),

  a(i) = a(j) => A000010(i) = A000010(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557

A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));

A322351(n) = min(A003557(n), A173557(n));

A322352(n) = max(A003557(n), A173557(n));

v322355 = rgs_transform(vector(up_to, n, [A322351(n), A322352(n)]));

A322355(n) = v322355[n];

CROSSREFS

Cf. A000010, A003557, A173557, A295887, A322320, A322321, A322351, A322352.

Sequence in context: A103391 A331743 A178804 * A242112 A211316 A280226

Adjacent sequences:  A322352 A322353 A322354 * A322356 A322357 A322358

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 05 2018

STATUS

approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)