%I #8 Sep 08 2022 08:46:24

%S 1,14,22,38,46,56,62,86,94,110,118,134,142,150,158,166,184,206,214,

%T 254,262,278,286,302,326,334,342,358,374,382,398,422,430,446,454,478,

%U 486,494,502,504,526,542,566,568,612,614,622,638,646,662,670,694,718,726

%N Numbers m such that gcd(sigma(m), pod(m)) = tau(m) where tau(k) = the number of divisors of k (A000005), sigma(k) = the sum of the divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).

%C Numbers n such that A306682(n) = A000005(n).

%e 14 is a term because gcd(sigma(14), pod(14)) = gcd(24, 196) = 4 = tau(14).

%o (Magma) [n: n in [1..10^5] | GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]) eq NumberOfDivisors(n)]

%o (PARI) isok(n) = my(d=divisors(n)); gcd(vecsum(d), vecprod(d)) == #d; \\ _Michel Marcus_, Mar 05 2019

%Y Cf. A000005, A000203, A007955, A306682.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Mar 05 2019