A373703 a(n) = A062760(n)*A066636(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 10, 1, 1, 1, 36, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100, 1, 1, 1, 22, 15, 1, 1, 216, 1, 10, 1, 26, 1, 36, 1, 196, 1, 1, 1, 30, 1, 1, 21, 1, 1, 1, 1, 34, 1, 1, 1, 6, 1, 1, 15, 38, 1, 1, 1, 1000

Offset

1,12

Comments

If n has unequal prime exponents (a term in A059404), then a(n) > 1; otherwise a(n) = 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

For n > 1, a(n) = A007947(n)^k where k is the difference between the greatest and least exponents in the prime power factorization of n.

Example

a(12) = A062760(12)*A066636(12) = 2*3 = 6.
a(45) = A062760(45)*A066636(45) = 3*5 = 15.

Mathematica

Table[Function[{r, s}, r^(Max[s] - Min[s])] @@ {Times @@ #[[All, 1]], #[[All, -1]]} &@ FactorInteger[n], {n, 120}] (* Michael De Vlieger, Jun 13 2024 *)

Prog

(PARI) a(n) = if (n==1, 1, my(f=factor(n)); (factorback(f[, 1]))^(vecmax(f[, 2])-vecmin(f[, 2]))); \\ Michel Marcus, Jun 14 2024

Crossrefs

Cf. A007947, A059404, A062760, A066636.

Sequence in context: A324396 A234959 A325471 * A167155 A369465 A268731

Adjacent sequences: A373700 A373701 A373702 * A373704 A373705 A373706

Keyword

nonn

Author

David James Sycamore, Jun 13 2024

Status

approved