A349006 a(1) = 1; for n > 1, a(n) is the smallest number m such that sigma(m) = tau(m)^n or 0 if no such m exists.

1, 3, 7, 217, 31, 3937, 127, 57337, 253921, 917497, 3670009, 16252897, 8191, 61079603913818329, 1073602561, 4294434817, 131071, 66571993057, 524287, 1208766717309082486038529, 9222228542614937599, 17590038552577, 500367932999371587367, 281472829095937, 1125897758834689

Offset: 1

Author

Jaroslav Krizek, Nov 05 2021

Keywords

• nonn

Comments

See A051281 for numbers m such that sigma(m) = tau(m)^k where k = integer.

a(n) = 0 for n = 76, 81, ...

Examples

			a(4) = 217 because 217 is the smallest number m such that sigma(m) = tau(m)^4; sigma(217) = 256 = tau(217)^4  = 4^4.
		

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A051281, A334455, A349007.

Programs

Magma

[1] cat [Min([m: m in[2..10^6] | &+Divisors(m) eq #Divisors(m)^n]): n in [2..10]]

Mathematica

Table[Block[{m = n}, While[#2 != #1^n & @@ DivisorSigma[{0, 1}, m], m++]; m], {n, 10}] (* Michael De Vlieger, Nov 05 2021 *)