A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

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

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A278221(n), A336158(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(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; };
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)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A000265(n) = (n>>valuation(n, 2));
A336158(n) = A046523(A000265(n));
Aux336148(n) = [A278221(n), A336158(n)];
v336148 = rgs_transform(vector(up_to, n, Aux336148(n)));
A336148(n) = v336148[n];

Crossrefs

Cf. A000265, A046523, A064989, A122111, A278221, A336158.

Cf. also A286621, A318890, A324400, A336146, A336149, A336159.

Sequence in context: A323234 A336156 A336474 * A336149 A336146 A324531

Adjacent sequences: A336145 A336146 A336147 * A336149 A336150 A336151

Keyword

nonn

Author

Antti Karttunen, Jul 12 2020

Status

approved