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A331186
Exponent of the highest power of prime(A067004(n)) which divides n, where A067004 is the ordinal transform of number of divisors of n (A000005).
3
0, 1, 1, 2, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 4, 1, 2, 1, 1, 0, 0, 1, 3, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 4, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 6, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0
OFFSET
1,4
LINKS
FORMULA
a(n) = A286561(n, A000040(A067004(n))), where A286561(n,k) gives the k-valuation of n.
MATHEMATICA
b[_] = 0;
A067004[n_] := A067004[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
a[n_] := IntegerExponent[n, Prime[A067004[n]]];
Array[a, 105] (* Jean-François Alcover, Dec 21 2021 *)
PROG
(PARI)
up_to = 65537;
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; };
v067004 = ordinal_transform(vector(up_to, n, numdiv(n)));
A067004(n) = v067004[n];
A331186(n) = valuation(n, prime(A067004(n)));
CROSSREFS
Cf. also A331185, A331187.
Sequence in context: A117162 A277045 A146061 * A375847 A372504 A135936
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 12 2020
STATUS
approved