A331187 a(n) is n divided by the highest power of prime(A067004(n)) which divides it, where A067004 is the ordinal transform of number of divisors of n (A000005).

1, 1, 1, 1, 1, 3, 1, 8, 1, 2, 1, 3, 1, 2, 15, 1, 1, 2, 1, 4, 21, 22, 1, 3, 1, 26, 27, 4, 1, 10, 1, 32, 33, 34, 35, 9, 1, 38, 39, 8, 1, 6, 1, 44, 45, 46, 1, 3, 1, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 15, 1, 62, 63, 1, 65, 66, 1, 68, 69, 70, 1, 8, 1, 74, 75, 76, 77, 78, 1, 80, 1, 82, 1, 84, 85, 86, 87, 88, 1, 90

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = n / (A000040(A067004(n))^A331186(n)).

Mathematica

b[_] = 0;
A067004[n_] := A067004[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
A331186[n_] := IntegerExponent[n, Prime[A067004[n]]];
a[n_] := n/(Prime[A067004[n]]^A331186[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];
A331187(n) = { my(p=prime(A067004(n))); n/(p^valuation(n, p)); };

Crossrefs

Cf. A000040, A067004, A331186.

Cf. also A331185.

Sequence in context: A276168 A165498 A195731 * A154294 A059526 A355828

Adjacent sequences: A331184 A331185 A331186 * A331188 A331189 A331190

Keyword

nonn

Author

Antti Karttunen, Jan 12 2020

Status

approved