A232445 Numbers n such that sigma(n) and sigma(n^2) are squares.

1, 11177320, 182937066, 159839399818, 166474679436

Offset

1,2

Comments

Intersection of A006532 and A008847.

sigma(a(6)) >= 10^12. - Hiroaki Yamanouchi, Sep 26 2014

Links

Table of n, a(n) for n=1..5.

Example

sigma(a(2)) = (64*9*5*2)^2 and sigma(a(2)^2) = (3*7*13*19*31*127)^2.
sigma(a(3)) = (64*9*5*7)^2 and sigma(a(3)^2) = (3*7*13*37*61*499)^2.
sigma(a(4)) = (256*9*5*47)^2 and sigma(a(4)^2) = (3*49*13*19*37*43*61*67)^2.
sigma(a(5)) = (16*3*7*121*17)^2 and sigma(a(5)^2) = (3*49*13*31*61*109*757)^2.

Prog

(PARI) isok(n) = issquare(sigma(n)) && issquare(sigma(n^2)); \\ Michel Marcus, Sep 24 2014

Crossrefs

Cf. A000203 (sigma: sum of divisors of n), A006532, A008847, A232444.

Sequence in context: A206519 A270491 A331360 * A187375 A219749 A219750

Adjacent sequences: A232442 A232443 A232444 * A232446 A232447 A232448

Keyword

nonn,hard,more

Author

Alex Ratushnyak, Nov 24 2013

Extensions

a(4) from Hiroaki Yamanouchi, Sep 24 2014

a(5) from Hiroaki Yamanouchi, Sep 26 2014

Status

approved