proposed

approved

editing

proposed

Cf. A046523, A162642, A248663, A335423, A335425.

Antti Karttunen, <a href="/A335424/b335424.txt">Table of n, a(n) for n = 1..65537</a>

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A162642(i) = A162642(j).

Cf. A046523, A162642, A248663, A335423.

Cf. also A286622, A305800.

allocated Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335423(i)) = A046523(A335423(j)) for Antti Karttunenall i, j >= 1.

1, 2, 2, 1, 2, 3, 2, 2, 1, 4, 2, 2, 2, 4, 3, 1, 2, 2, 2, 2, 4, 4, 2, 3, 1, 4, 2, 2, 2, 5, 2, 2, 4, 4, 3, 1, 2, 4, 4, 4, 2, 6, 2, 2, 2, 4, 2, 2, 1, 2, 4, 2, 2, 3, 4, 4, 4, 4, 2, 3, 2, 4, 2, 1, 4, 6, 2, 2, 4, 6, 2, 2, 2, 4, 2, 2, 3, 6, 2, 2, 1, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 3, 2, 2, 2, 1, 2, 6, 2, 4, 5

1,2

(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; };

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

A248663(n) = A048675(core(n));

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

A335423(n) = A005940(1+A248663(n));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };

v335424 = rgs_transform(vector(up_to, n, A046523(A335423(n))));

A335424(n) = v335424[n];

Cf. A046523, A248663, A335423.

Cf. also A286622.

allocated

nonn

Antti Karttunen, Jun 13 2020

approved

editing

allocated for Antti Karttunen

allocated

approved