A373593 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A046523(A248909(n)), A046523(A343430(n))].

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 7, 12, 6, 13, 5, 14, 7, 15, 16, 10, 5, 17, 4, 12, 18, 19, 5, 20, 7, 21, 6, 10, 12, 22, 7, 12, 16, 23, 5, 24, 7, 15, 14, 10, 5, 25, 26, 15, 6, 19, 5, 27, 10, 28, 16, 10, 5, 29, 7, 12, 30, 31, 12, 20, 7, 15, 6, 32, 5, 33, 7, 12, 11, 19, 12, 24, 7, 34, 35, 10, 5, 36, 10, 12, 6, 23, 5, 37, 38, 15, 16, 10, 12, 39, 7, 40, 14, 41

Offset: 1

Author

Antti Karttunen, Jun 13 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the function f given in the definition.

For all i, j >= 1:

a(i) = a(j) => A373595(i) = A373595(j),

a(i) = a(j) => A353815(i) = A353815(j),

a(i) = a(j) => A353816(i) = A353816(j).

Links

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

Crossrefs

Cf. A007949, A046523, A248909, A343430.

Cf. A353815, A353816, A373595.

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; };
A007949(n) = valuation(n,3);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A248909(n) = { my(f=factor(n)); for(k=1, #f~, if(1!=(f[k,1]%3), f[k,1]=1)); factorback(f); };
A343430(n) = { my(f=factor(n)); for(k=1, #f~, if(2!=(f[k,1]%3), f[k,1]=1)); factorback(f); };
Aux373593(n) = if(n<3, n, [A007949(n), A046523(A248909(n)), A046523(A343430(n))]);
v373593 = rgs_transform(vector(up_to, n, Aux373593(n)));
A373593(n) = v373593[n];