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A327970
Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(n) = A003415(j) and A327936(i) = A327936(j) for all i, j.
2
1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 11, 2, 19, 2, 20, 21, 22, 23, 24, 2, 12, 25, 26, 2, 27, 2, 28, 29, 30, 2, 31, 21, 32, 33, 34, 2, 35, 25, 36, 37, 19, 2, 36, 2, 38, 39, 40, 41, 42, 2, 43, 44, 45, 2, 46, 2, 29, 47, 20, 41, 48, 2, 49, 50, 51, 2, 52, 37, 32, 53, 54, 2, 55, 33, 56, 57, 58, 59, 60, 2, 61, 62, 54, 2, 63, 2, 64, 48
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A003415(n), A327936(n)].
For all i, j:
a(i) = a(j) => A256750(i) = A256750(j),
a(i) = a(j) => A327932(i) = A327932(j).
LINKS
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; };
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
Aux327970(n) = [A003415(n), A327936(n)];
v327970 = rgs_transform(vector(up_to, n, Aux327970(n)));
A327970(n) = v327970[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved