A131904 Smallest positive integer k with the same number of divisors as the n-th integer for which such a k exists.

2, 2, 2, 6, 4, 6, 2, 2, 6, 6, 2, 12, 2, 12, 6, 6, 2, 4, 6, 6, 12, 2, 24, 2, 12, 6, 6, 6, 2, 6, 6, 24, 2, 24, 2, 12, 12, 6, 2, 4, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 2, 6, 12, 6, 24, 2, 12, 6, 24, 2, 60, 2, 6, 12, 12, 6, 24, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24, 2

Offset: 1

Author

Peter Pein (petsie(AT)dordos.net), Jul 26 2007

Keywords

• easy
• nonn

Examples

			a(4)=6 because A131903(4)=8, which has four divisors, and 6 is the least positive integer with four divisors
		

Crossrefs

Cf. A069822, A131902-A131908.

Programs

Mathematica

Clear[tmp]; Function[n, If[Head[ #1] === tmp, #1 = n; Unevaluated[Sequence[]], # ] & [tmp[DivisorSigma[0, n]]]] /@ Range[64]

PARI

lista(nn) = {for (n=1, nn, my(nd = numdiv(n)); for (k=1, n-1, if (numdiv(k) == nd, print1(k, ", "); break);););} \\ Michel Marcus, Apr 03 2015

Formula

a(n)=min(k>0, k has the same number of divisors as A131903(n))

Extensions

More terms from Michel Marcus, Apr 03 2015