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A322816
Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A048675(n) for all other numbers, except f(n) = -1 if n is an odd prime.
5
1, 2, 3, 4, 3, 5, 3, 5, 6, 7, 3, 6, 3, 8, 9, 6, 3, 7, 3, 9, 10, 11, 3, 7, 12, 13, 9, 10, 3, 14, 3, 7, 15, 16, 17, 9, 3, 18, 19, 14, 3, 20, 3, 15, 12, 21, 3, 9, 22, 8, 23, 19, 3, 14, 24, 20, 25, 26, 3, 12, 3, 27, 17, 9, 28, 29, 3, 23, 30, 31, 3, 14, 3, 32, 10, 25, 33, 34, 3, 12, 12, 35, 3, 17, 36, 37, 38, 29, 3, 8, 39, 30, 40, 41, 42, 14, 3, 11, 24, 10, 3, 43, 3, 34, 44
OFFSET
1,2
COMMENTS
For all i, j > 1:
A323078(i) = A323078(j) => a(i) = a(j),
a(i) = a(j) => A322812(i) = A322812(j),
a(i) = a(j) => A322869(i) = A322869(j).
LINKS
PROG
(PARI)
up_to = 4096;
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; };
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A322816aux(n) = if((n>2)&&isprime(n), -1, A048675(n));
v322816 = rgs_transform(vector(up_to, n, A322816aux(n)));
A322816(n) = v322816[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 27 2018
STATUS
approved