login
A167401
a(n) is the smallest number k such that n*k has twice as many divisors as k.
3
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
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
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