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A326193 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,sigma(n)) * (-1)^[gcd(n,sigma(n))==n]. 3
1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 5, 2, 4, 6, 2, 2, 6, 2, 4, 2, 4, 2, 7, 2, 4, 2, 8, 2, 9, 2, 2, 6, 4, 2, 2, 2, 4, 2, 10, 2, 9, 2, 5, 6, 4, 2, 5, 2, 2, 6, 4, 2, 9, 2, 11, 2, 4, 2, 7, 2, 4, 2, 2, 2, 9, 2, 4, 6, 4, 2, 6, 2, 4, 2, 5, 2, 9, 2, 4, 2, 4, 2, 12, 2, 4, 6, 5, 2, 13, 14, 5, 2, 4, 15, 7, 2, 2, 6, 2, 2, 9, 2, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of function f, defined as f(n) = -A009194(n) = -n when n is one of multiply-perfect numbers (A007691), otherwise f(n) = A009194(n) = gcd(n,sigma(n)).
For all i, j:
a(i) = a(j) => A326194(i) = A326194(j).
LINKS
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; };
Aux326193(n) = { my(u=gcd(n, sigma(n))); u*((-1)^(u==n)); };
v326193 = rgs_transform(vector(up_to, n, Aux326193(n)));
A326193(n) = v326193[n];
CROSSREFS
Sequence in context: A359212 A320018 A327162 * A327163 A324538 A305976
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 24 2019
STATUS
approved

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Last modified March 30 04:14 EDT 2024. Contains 371289 sequences. (Running on oeis4.)