A324538 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A324537(n) for all other numbers, except f(1) = 0.

1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 5, 2, 6, 4, 2, 2, 7, 2, 4, 6, 8, 2, 9, 2, 10, 2, 6, 2, 11, 2, 2, 8, 12, 6, 13, 2, 14, 10, 15, 2, 16, 2, 8, 15, 17, 2, 18, 2, 19, 12, 10, 2, 20, 8, 6, 14, 21, 2, 22, 2, 23, 6, 2, 10, 24, 2, 12, 17, 25, 2, 26, 2, 27, 19, 14, 8, 28, 2, 29, 2, 30, 2, 31, 12, 32, 21, 8, 2, 33, 10, 17, 23, 34, 14, 35, 2, 36, 8, 37, 2, 38, 2, 10, 25

Offset: 1

Author

Antti Karttunen, Mar 07 2019

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A069513(i) = A069513(j),

a(i) = a(j) => A324191(i) = A324191(j).

Links

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

Crossrefs

Cf. A000961 (positions of terms <= 2), A069513, A297167, A324191, A324537.

Cf. also A300827, A324181, A324203, A324196, A324197.

Programs

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; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A324537(n) = { my(m=1); fordiv(n, d, if(d>2, m *= prime(A297167(d)))); A003557(m); };
Aux324538(n) = if(1==n,0,A324537(n));
v324538 = rgs_transform(vector(up_to,n,Aux324538(n)));
A324538(n) = v324538[n];