A306667 Numbers m such that lcm(tau(m), m) = sigma(m) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of the divisors of k (A000005).

1, 6, 32760, 51001180160, 54530444405217553992377326508106948362108928, 133821156044600922812153118065015159487725568, 42274041475824304453686528060845522019324411248640, 48949643430560436794021629524876790263031553747866371344635527168

Offset: 1

Author

Jaroslav Krizek, Mar 04 2019

Keywords

• nonn
• hard

Comments

Numbers m such that A009230(m) = A000203(m).

Subsequence of multiply-perfect numbers (A007691).

Examples

			6 is a term because lcm(tau(6), 6) = lcm(4, 6) = 12 = sigma(6).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..11 (from A007691 data)

Crossrefs

Cf. A000005, A000203, A009230.

Cf. A069810 (gcd(k, sigma(k)) = tau(k)).

Programs

Magma

[n: n in [1..100000] | LCM(NumberOfDivisors(n), n) eq SumOfDivisors(n)]

Extensions

a(4)-a(8) computed from A007691 data by Giovanni Resta, Mar 05 2019