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A330755
Number of values of k, 1 <= k <= n, with A034684(k) = A034684(n), where A034684 gives the smallest unitary divisor of n that is larger than 1.
1
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 3, 1, 1, 5, 1, 2, 4, 6, 1, 5, 1, 7, 1, 3, 1, 8, 1, 1, 6, 9, 2, 4, 1, 10, 7, 3, 1, 11, 1, 5, 4, 12, 1, 8, 1, 13, 9, 6, 1, 14, 5, 2, 10, 15, 1, 11, 1, 16, 3, 1, 6, 17, 1, 7, 12, 18, 1, 2, 1, 19, 13, 8, 4, 20, 1, 7, 1, 21, 1, 14, 8, 22, 15, 3, 1, 23, 5, 9, 16, 24, 9, 17, 1, 25, 2, 10, 1, 26, 1, 4, 18
OFFSET
1,6
COMMENTS
Ordinal transform of A034684.
LINKS
MATHEMATICA
A034684[n_] := With[{f = FactorInteger[n]}, Min[f[[All, 1]]^f[[All, 2]]]];
Module[{b}, b[_] = 0;
a[n_] := With[{t = A034684[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)
PROG
(PARI)
up_to = 65537;
A034684(n) = if(1==n, n, my(f=factor(n)); vecmin(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ After code in A034699
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
v330755 = ordinal_transform(vector(up_to, n, A034684(n)));
A330755(n) = v330755[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 30 2019
STATUS
approved