A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.

1, 2, 2, 3, 4, 5, 2, 6, 3, 7, 2, 8, 2, 5, 7, 9, 2, 8, 2, 10, 5, 5, 2, 11, 12, 5, 6, 8, 2, 13, 2, 14, 5, 5, 7, 15, 2, 5, 5, 16, 2, 17, 2, 8, 10, 5, 2, 18, 3, 19, 5, 8, 2, 11, 7, 11, 5, 5, 2, 20, 2, 5, 8, 21, 7, 17, 2, 8, 5, 13, 2, 22, 2, 5, 19, 8, 5, 17, 2, 23, 9, 5, 2, 24, 7, 5, 5, 11, 2, 20, 5, 8, 5, 5, 7, 25, 2, 8, 8, 26, 2, 17, 2, 11, 13

Offset: 1

Author

Antti Karttunen, Dec 15 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A112765(n)].

For all i, j:

A379001(i) = A379001(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A046523, A112765, A379001.

Cf. also A305891, A305893.

Programs

PARI

up_to = 100000;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v379002 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n,5)]));
A379002(n) = v379002[n];