A373151 Lexicographically earliest infinite sequence such that a(i) = a(j) => A083345(i) = A083345(j) and A373145(i) = A373145(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 6, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 15, 31, 2, 32, 6, 9, 33, 34, 2, 35, 27, 36, 37, 20, 2, 38, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 15, 2, 47, 16, 48, 42, 49, 2, 50, 8, 51, 2, 52, 37, 53, 54, 55, 2, 29, 56, 57, 58, 59, 60, 28, 2, 16, 31, 61

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A083345(n), A373145(n)].

For all i, j >= 1:

A373150(i) = A373150(j) => a(i) = a(j),

a(i) = a(j) => A369001(i) = A369001(j),

a(i) = a(j) => A369004(i) = A369004(j),

a(i) = a(j) => A373143(i) = A373143(j).

Links

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

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A373145(n) = gcd(A003415(n), A276085(n));
Aux373151(n) = [A083345(n), A373145(n)];
v373151 = rgs_transform(vector(up_to, n, Aux373151(n)));
A373151(n) = v373151[n];

Crossrefs

Cf. A003415, A002110, A083345, A276085, A373145.

Cf. A369001, A369004, A373143, A373150.

Sequence in context: A329351 A319709 A293226 * A328315 A327970 A369448

Adjacent sequences: A373148 A373149 A373150 * A373152 A373153 A373154

Keyword

nonn

Author

Antti Karttunen, May 27 2024

Status

approved