A290479 Product of nonprime squarefree divisors of n.

1, 1, 1, 1, 1, 6, 1, 1, 1, 10, 1, 6, 1, 14, 15, 1, 1, 6, 1, 10, 21, 22, 1, 6, 1, 26, 1, 14, 1, 27000, 1, 1, 33, 34, 35, 6, 1, 38, 39, 10, 1, 74088, 1, 22, 15, 46, 1, 6, 1, 10, 51, 26, 1, 6, 55, 14, 57, 58, 1, 27000, 1, 62, 21, 1, 65, 287496, 1, 34, 69, 343000, 1, 6, 1, 74, 15, 38, 77, 474552, 1, 10

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A078599(n)/A007947(n).

a(n) = rad(n)^(d(rad(n))/2-1), where d() is the number of divisors of n (A000005) and rad() is the squarefree kernel of n (A007947).

a(n) = 1 if n is a prime power.

Example

a(30) = 27000 because 30 has 8 divisors {1, 2, 3, 5, 6, 10, 15, 30} among which 5 are nonprime squarefree {1, 6, 10, 15, 30} and 1*6*10*15*30 = 27000.

Mathematica

Table[Product[d, {d, Select[Divisors[n], !PrimeQ[#] && SquareFreeQ[#] &]}], {n, 80}]
Table[Last[Select[Divisors[n], SquareFreeQ]]^(DivisorSigma[0, Last[Select[Divisors[n], SquareFreeQ]]]/2 - 1), {n, 80}]

Prog

(PARI) A290479(n) = if(1==n, n, my(r=factorback(factorint(n)[, 1])); (r^((numdiv(r)/2)-1))); \\ Antti Karttunen, Aug 06 2018

Crossrefs

Cf. A000005, A000469, A006881 (fixed points), A007947, A007955, A007956, A061537, A062758, A078599, A087652, A126192, A136655, A183091, A284118.

Sequence in context: A340677 A340679 A166142 * A304404 A290480 A183092

Adjacent sequences: A290476 A290477 A290478 * A290480 A290481 A290482

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 03 2017

Status

approved