OFFSET
1,2
COMMENTS
Restricted growth sequence transform of triple [A010873(A020639(n)), A032742(n), A319710(n)], or equally, of ordered pair [A319714(n), A319710(n)].
Here any nontrivial equivalence classes (that is, when we exclude the singleton classes and two infinite classes of A002144 and A002145), like the example shown, may not contain any even numbers, nor any numbers from A283050. See additional comments in A319717 and A319994.
For all i, j:
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
EXAMPLE
For n = 33 (3*11) and n = 77 (7*11), the modulo 4 residue of the smallest prime factor is 3, and the largest proper divisors (A032742) is also equal 11, and the smallest prime factor is unitary. Thus a(33) = a(77) (= 25, a running count value allotted by rgs-transform).
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; };
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A319710(n) = ((n>1)&&(factor(n)[1, 2]>1));
A320004(n) = v320004[n];
CROSSREFS
Cf. also A319717 (analogous sequence for modulo 6 residues).
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 04 2018
STATUS
approved