A138221 a(n) = the smallest divisor of n that is >= the number of positive divisors of n.

1, 2, 3, 4, 5, 6, 7, 4, 3, 5, 11, 6, 13, 7, 5, 8, 17, 6, 19, 10, 7, 11, 23, 8, 5, 13, 9, 7, 29, 10, 31, 8, 11, 17, 5, 9, 37, 19, 13, 8, 41, 14, 43, 11, 9, 23, 47, 12, 7, 10, 17, 13, 53, 9, 5, 8, 19, 29, 59, 12, 61, 31, 7, 8, 5, 11, 67, 17, 23, 10, 71, 12, 73, 37, 15, 19, 7, 13, 79, 10, 9

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = n for all primes plus the integers {1, 4, 6}. - Robert G. Wilson v

Example

There are four positive divisors of 15: (1,3,5,15). The smallest of these divisors that is >=4 is 5; so a(15) = 5.

Maple

with(numtheory): a:=proc(n) local dn, i: dn:=divisors(n): for i while dn[i] < tau(n) do end do: dn[i] end proc: seq(a(n), n=1..60); # Emeric Deutsch, Mar 17 2008

Mathematica

f[n_] := First@Select[Divisors@n, # >= DivisorSigma[0, n] &]; Array[f, 81] (* Robert G. Wilson v *)

Prog

(PARI) a(n) = {my(d = divisors(n), nd = #d); for(i = 1, nd, if(d[i] >= nd, return(d[i]))); } \\ Amiram Eldar, Apr 15 2024

Crossrefs

Cf. A138222, A138223, A138224, A000005.

Sequence in context: A115871 A366383 A366382 * A038388 A366392 A272573

Adjacent sequences: A138218 A138219 A138220 * A138222 A138223 A138224

Keyword

nonn,changed

Author

Leroy Quet, Mar 06 2008

Extensions

More terms from Emeric Deutsch, Robert G. Wilson v and Erich Friedman, Mar 17 2008

Status

approved