A324555 - OEIS

A324555

a(n) = the smallest number m such that gcd(tau(m), pod(m)) = n where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).

1, 2, 9, 6, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 120, 18939904, 180, 94633984, 240, 35721, 11264, 2218786816, 360, 10000, 53248, 900, 1344, 225754218496, 720, 1031865892864, 840, 7144929, 1114112, 1960000, 1260, 94076963651584, 4980736

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OFFSET

1,2

COMMENTS

a(n) = the smallest number m such that A306671(m) = n.

If a(17) exists, it must be bigger than 10^7.

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

For n=3; a(3) = 9 because gcd(tau(9), pod(9)) = gcd (3, 27) = 3 and 9 is the smallest.

MATHEMATICA

Array[Block[{m = 1}, While[GCD[DivisorSigma[0, m], Times @@ Divisors@ m] != #, m++]; m] &, 16] (* Michael De Vlieger, Mar 24 2019 *)