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A138221
a(n) = the smallest divisor of n that is >= the number of positive divisors of n.
4
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 06 2008
EXTENSIONS
More terms from Emeric Deutsch, Robert G. Wilson v and Erich Friedman, Mar 17 2008
STATUS
approved