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A322311
Lexicographically earliest such sequence a that a(i) = a(j) => A322310(i) = A322310(j) for all i, j.
2
1, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 3, 3, 9, 3, 5, 3, 10, 3, 7, 3, 11, 3, 3, 3, 7, 3, 7, 3, 12, 3, 3, 3, 13, 3, 3, 3, 14, 3, 5, 3, 2, 3, 7, 3, 15, 3, 3, 3, 7, 3, 7, 3, 2, 3, 7, 3, 16, 3, 3, 3, 17, 3, 7, 3, 3, 3, 7, 3, 18, 3, 3, 3, 3, 3, 7, 3, 19, 3, 7, 3, 20, 3, 3, 3, 8, 3, 3, 3, 2, 3, 3, 3, 21, 3, 3, 3, 5, 3, 7, 3, 2, 3
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of A322310.
For all i, j: a(i) = a(j) => A014197(i) = A014197(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; };
A320000sq(n, k) = if(1==n, if(1==k, 2, 1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ Cf. A320000
A322310(n) = if(1==n, 3, my(m=1); fordiv(n, d, my(s, p=d+1, q=n/d); if(isprime(p) && (s = sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))), m *= prime(s))); (m));
v322311 = rgs_transform(vector(up_to, n, A322310(n)));
A322311(n) = v322311[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 03 2018
STATUS
approved