A322805 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(1)=0, f(2)=1, f(n)=-1 for odd primes, and f(n) = A252463(n) for any other number.

1, 2, 3, 4, 3, 5, 3, 6, 6, 7, 3, 8, 3, 9, 8, 10, 3, 11, 3, 12, 12, 13, 3, 14, 11, 15, 10, 16, 3, 17, 3, 18, 16, 19, 17, 20, 3, 21, 22, 23, 3, 24, 3, 22, 14, 25, 3, 26, 27, 27, 28, 28, 3, 29, 24, 30, 31, 32, 3, 33, 3, 34, 23, 35, 36, 36, 3, 31, 37, 38, 3, 39, 3, 40, 20, 37, 38, 41, 3, 42, 18, 43, 3, 44, 41, 45, 46, 47, 3, 48, 49, 46, 50, 51, 52, 53, 3, 54, 30, 55, 3, 52, 3, 56, 33

Offset

1,2

Comments

For all i, j:

a(i) = a(j) => A319694(i) = A319694(j),

a(i) = a(j) => A319699(i) = A319699(j),

a(i) = a(j) => A319700(i) = A319700(j),

a(i) = a(j) => A319703(i) = A319703(j),

a(i) = a(j) => A319989(i) = A319989(j),

a(i) = a(j) => A320110(i) = A320110(j) => A320111(i) = A320111(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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A252463(n) = if(!(n%2), n/2, A064989(n));
A322805aux(n) = if(n<=2, n-1, if(isprime(n), -1, A252463(n)));
v322805 = rgs_transform(vector(up_to, n, A322805aux(n)));
A322805(n) = v322805[n];

Crossrefs

Cf. A252463.

Cf. A319694, A319699, A319700, A319703, A319989, A320110, A320111.

Cf. also A322807, A322809.

Sequence in context: A355833 A319339 A322807 * A322809 A366384 A291761

Adjacent sequences: A322802 A322803 A322804 * A322806 A322807 A322808

Keyword

nonn

Author

Antti Karttunen, Dec 26 2018

Status

approved