A336147 - OEIS

A336147

Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A020639(n), A278221(n)].

For all i, j:

A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j),

a(i) = a(j) => A243055(i) = A243055(j),

a(i) = a(j) => A336150(i) = A336150(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; };

A020639(n) = if(1==n, n, factor(n)[1, 1]);

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));

Aux336147(n) = [A020639(n), A278221(n)];

v336147 = rgs_transform(vector(up_to, n, Aux336147(n)));

A336147(n) = v336147[n];

CROSSREFS

Cf. A020639, A046523, A122111, A278221.

Cf. also A243055, A286621, A318891, A324400, A336146, A336148, A336149, A336150.

First differs from A322590 at a(70) = 28 instead of 44.