login
A328469
Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A046523(i) = A046523(j) for all i, j.
3
1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 10, 11, 12, 6, 13, 14, 15, 11, 16, 11, 13, 6, 17, 18, 19, 6, 20, 11, 21, 22, 23, 24, 13, 6, 25, 26, 27, 6, 13, 18, 28, 22, 29, 11, 30, 6, 31, 32, 33, 11, 13, 11, 34, 18, 25, 18, 13, 6, 35, 36, 37, 6, 30, 38, 25, 22, 39, 11, 13, 22, 40, 41, 42, 6, 30, 11, 43, 22, 44, 32, 45, 6, 46, 36, 25, 6, 13, 18, 47, 36, 43, 11, 13, 6, 25, 48, 49, 11, 30, 26, 50, 22, 51, 18, 52
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A020639(n), A046523(n)], where A020639(n) gives the smallest prime factor of n, while A046523(n) gives the prime signature of n.
For all i, j: a(i) = a(j) => A291761(i) = A291761(j).
LINKS
PROG
(PARI)
up_to = 100000;
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(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
Aux328469(n) = [A020639(n), A046523(n)];
v328469 = rgs_transform(vector(up_to, n, Aux328469(n)));
A328469(n) = v328469[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 19 2019
STATUS
approved