A323240 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A001222(n), A323244(n)] for n > 1, and f(1) = 0.

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

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f, where f(1) = 0 and f(n) = [A001222(n), A323244(n)] for n > 1.

Equally, restricted growth sequence transform of function f, where f(1) = 0 and f(n) = A318310(A156552(n)) for n > 1.

For all i, j:

a(i) = a(j) => A323245(i) = A323245(j), [Equally: A323244(i) = A323244(j)]

a(i) = a(j) => A323246(i) = A323246(j). [Equally: A323248(i) = A323248(j)]

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A001222, A156552, A318310, A323244, A323245, A323246, A323248.

Cf. also A323168.

Programs

PARI

up_to = 1024;
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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));
A323240aux(n) = if(1==n,-1,[bigomega(n),A323244(n)]);
v323240 = rgs_transform(vector(up_to, n, A323240aux(n)));
A323240(n) = v323240[n];