A167401 a(n) is the smallest number k such that n*k has twice as many divisors as k.

1, 1, 2, 1, 12, 1, 4, 3, 20, 1, 72, 1, 28, 45, 8, 1, 108, 1, 160, 63, 44, 1, 288, 5, 52, 9, 224, 1, 10800, 1, 16, 99, 68, 175, 864, 1, 76, 117, 800, 1, 21168, 1, 352, 675, 92, 1, 1152, 7, 400, 153, 416, 1, 648, 275, 1568, 171, 116, 1, 259200

Offset

2,3

Comments

a(n) is 1 for all prime numbers n.

From Robert Israel, Feb 09 2017: (Start)

All prime factors of a(n) divide n.

If n=p^k is a prime power, a(n) = p^(k-1).

If n=p*q with p<q is in A006881, a(n) = p^2*q. (End)

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Maple

A167401 := proc(n) if isprime(n) then 1; else for a from 2 do if numtheory[tau](n*a) = 2*numtheory[tau](a) then return a ; end if; end do ; fi; end: seq(A167401(n), n=2..60) ; # R. J. Mathar, Nov 04 2009

Mathematica

tmd[n_]:=Module[{a=1}, While[DivisorSigma[0, a*n]!=2DivisorSigma[0, a], a++]; a]; Array[tmd, 60, 2] (* Harvey P. Dale, Apr 20 2013 *)

Prog

(PARI) a(n) = {my(k=1); while (numdiv(n*k) != 2*numdiv(k), k++); k; } \\ Michel Marcus, Feb 10 2017

Crossrefs

Cf. A139315.

Sequence in context: A066818 A005730 A112284 * A069249 A128247 A161150

Adjacent sequences: A167398 A167399 A167400 * A167402 A167403 A167404

Keyword

nonn,look

Author

J. Lowell, Nov 02 2009

Extensions

Extended by Ray Chandler, Nov 10 2009

Extended beyond a(10) by R. J. Mathar, Nov 04 2009

Status

approved