A381925 Positive integers k which have at least one divisor d for which tau(k) = sigma(d).

1, 4, 6, 15, 20, 21, 27, 33, 39, 42, 45, 50, 51, 56, 57, 60, 64, 69, 70, 72, 75, 84, 87, 90, 93, 96, 105, 108, 111, 123, 126, 129, 132, 141, 144, 150, 154, 156, 159, 175, 177, 180, 182, 183, 189, 198, 201, 204, 213, 219, 220, 228, 231, 234, 237, 238, 245, 249, 266

Offset

1,2

Comments

Includes 3 * p for all primes p <> 3, 5^2 * p and 5 * p^2 for all primes p <> 5, 7 * p * q for distinct primes p, q <> 7, 12 * p for all primes p > 3, 16 * p^2 for all odd primes p. - Robert Israel, Mar 12 2025

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Example

15 is in the sequence because it has the 4 divisors 1, 3, 5, 15 and sigma(3) = 1 + 3 = 4.
60 is in the sequence because it has the 12 divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and sigma(6) = 1 + 2 + 3 + 6 = 12.

Maple

with(NumberTheory):
A381925:=proc(n)
    option remember;
    local k, d; 	
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do	
            for d in Divisors(k) do
                if sigma(d)=tau(k) then
                    return k
                fi
            od
        od
    fi;
end proc;
seq(A381925(n), n=1..59);

Mathematica

q[k_] := AnyTrue[Divisors[k], DivisorSigma[1, #] == DivisorSigma[0, k] &]; Select[Range[300], q] (* Amiram Eldar, Mar 12 2025 *)

Prog

(PARI) isok(k) = sumdiv(k, d, sigma(d) == numdiv(k)) >= 1; \\ Michel Marcus, Mar 12 2025

Crossrefs

Cf. A000005, A000203, A000396, A027750, A381926, A381927.

Sequence in context: A034771 A294457 A266883 * A034764 A119034 A100911

Adjacent sequences: A381921 A381922 A381923 * A381928 A381929 A381930

Keyword

nonn,new

Author

Felix Huber, Mar 12 2025

Status

approved