A231484 Numbers n such that n, sigma(n) and sigma(sigma(n)) are odd.

1, 81, 1476326929, 10994571025, 61436066769, 98551417041, 119582481249, 141447449025, 220545762129, 388895668225, 619568914129, 890560253025, 970952066161, 2580138650961, 3076652813521, 3739640454225, 4138876942929, 4758545225281, 9262289646801, 26494089912081

Offset: 1

Author

Vladimir Letsko, Nov 09 2013

Keywords

• nonn

Comments

Contains exactly odd terms of A008848.

Odd n is a term if and only if both n and sigma(n) are perfect squares.

Examples

			81 is a term because 81, sigma(81) = 121 and sigma(sigma(81)) = 133 are all odd.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..125
• Vladimir Letsko Mathematical Marathon, problem 180 (in Russian)

Crossrefs

Cf. A008848.

Programs

PARI

forstep(r=1, 5147241, 2, n=r^2; if(sigma(sigma(n))%2<>0, print1(n ", "))) \\ Donovan Johnson, Nov 09 2013

PARI

forstep(r=1, 5147241, 2, if(!isprime(r)&&issquare(sigma(n=r^2)), print1(n", "))) \\ Charles R Greathouse IV, Nov 12 2013

Extensions

a(5) corrected by Donovan Johnson, Nov 09 2013