A073182 Number of divisors of n which are not greater than the cubefree kernel of n.

1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 3, 2, 6, 2, 6, 4, 4, 2, 7, 3, 4, 3, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 7, 2, 8, 2, 6, 6, 4, 2, 7, 3, 6, 4, 6, 2, 6, 4, 7, 4, 4, 2, 12, 2, 4, 6, 3, 4, 8, 2, 6, 4, 8, 2, 11, 2, 4, 6, 6, 4, 8, 2, 8, 3, 4, 2, 12, 4, 4, 4, 7, 2, 12, 4, 6, 4, 4, 4, 7, 2, 6, 6, 9, 2, 8

Offset

1,2

Comments

a(n) >= A073184(n).

Links

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

Example

The cubefree kernel of 56 = 7*2^3 is 28 = 7*2^2 and the divisors <= 28 of 56 are {1, 2, 4, 7, 8, 14, 28}, therefore a(56) = 7.

Mathematica

Table[Function[k, DivisorSum[n, 1 &, # <= k &]]@ Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 0 :> p^Min[e, 2]], {n, 102}] (* Michael De Vlieger, Jul 18 2017 *)

Prog

(PARI) a007948(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = min(f[i, 2], 2)); factorback(f);
a(n) = my(cfk = a007948(n)); sumdiv(n, d, d<=cfk); \\ Michel Marcus, May 14 2015

Crossrefs

Cf. A000005, A007948, A073183, A073180.

Sequence in context: A196437 A106491 A073184 * A282446 A049599 A353898

Adjacent sequences: A073179 A073180 A073181 * A073183 A073184 A073185

Keyword

nonn

Author

Reinhard Zumkeller, Jul 19 2002

Status

approved