A374478 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j) and A364255(i) = A364255(j), for all i, j >= 1.

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 11, 12, 13, 5, 14, 5, 15, 16, 17, 5, 18, 19, 20, 21, 22, 5, 23, 5, 24, 25, 26, 27, 28, 5, 29, 30, 31, 5, 32, 5, 33, 34, 35, 5, 36, 37, 38, 39, 40, 5, 41, 42, 43, 44, 45, 5, 46, 5, 47, 48, 49, 50, 51, 5, 52, 53, 54, 5, 55, 5, 56, 57, 58, 59, 60, 5, 61, 62, 63, 5, 64, 65, 66, 67, 68, 5, 69, 70, 71, 72, 73, 39, 74, 5, 75, 76, 77, 5

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A348717(n), A364255(n)].

For all i, j >= 1:

A305900(i) = A305900(j) => a(i) = a(j),

a(i) = a(j) => A305891(i) = A305891(j),

a(i) = a(j) => A374477(i) = A374477(j).

Links

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

Index entries for sequences computed from indices in prime factorization

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; };
A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364255(n) = gcd(n, A163511(n));
Aux374478(n) = [A348717(n), A364255(n)];
v374478 = rgs_transform(vector(up_to, n, Aux374478(n)));
A374478(n) = v374478[n];

Crossrefs

Cf. A163511, A348717, A364255.

Cf. also A305891, A305897, A364297, A364949, A365392, A365423, A374477.

Differs from A374040 first at n=77, where a(77) = 59, while A374040(77) = 50.

Differs from A305900 first at n=95, where a(95) = 39, while A305900(95) = 74.

Sequence in context: A358230 A373594 A374040 * A305900 A287943 A305211

Adjacent sequences: A374475 A374476 A374477 * A374479 A374480 A374481

Keyword

nonn

Author

Antti Karttunen, Aug 07 2024

Status

approved