A272347 Least number divisible by n and by the number of its own divisors.

1, 2, 9, 8, 40, 12, 56, 8, 9, 40, 88, 12, 104, 56, 60, 80, 136, 18, 152, 40, 84, 88, 184, 24, 225, 104, 108, 56, 232, 60, 248, 96, 132, 136, 560, 36, 296, 152, 156, 40, 328, 84, 344, 88, 180, 184, 376, 96, 441, 450, 204, 104, 424, 108, 880, 56, 228, 232, 472, 60

Offset

1,2

Comments

By the sequence definition, all terms are refactorable numbers (A033950).

a(n) = n if and only if n is in A033950. - Robert Israel, Feb 15 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n=4, a(4)=8 because it is the smallest number divisible by 4 whose number of divisors (4) is also divisible by 4; 4 has 3 divisors and cannot be a term.

Maple

isA033950 := proc(n)
    if modp(n, numtheory[tau](n)) = 0 then
        true;
    else
        false;
    end if;
end proc:
A272347 := proc(n)
    local m;
    for m from 1 do
        if isA033950(m*n) then
            return m*n;
        end if;
    end do:
end proc:
seq(A272347(n), n=1..50) ; # R. J. Mathar, Apr 29 2016

Mathematica

f[n_] := Block[{m = n}, While[ Mod[m, DivisorSigma[0, m]] > 0, m += n];
m]; Array[f, 60] (* Robert G. Wilson v, Feb 15 2017 *)

Prog

(PARI) for(n=1, 75, k=n; while(!(k%n==0&&k%numdiv(k)==0), k++); print1(k ", "))

Crossrefs

Cf. A000005 (number of divisors), A033950 (refactorable numbers).

Sequence in context: A357993 A129194 A300780 * A371255 A214300 A092397

Adjacent sequences: A272344 A272345 A272346 * A272348 A272349 A272350

Keyword

nonn,look

Author

Waldemar Puszkarz, Apr 26 2016

Status

approved