A152921 a(n) = 2^(2p-1)/2, where p is A000043(n).

4, 16, 256, 4096, 16777216, 4294967296, 68719476736, 1152921504606846976, 1329227995784915872903807060280344576, 95780971304118053647396689196894323976171195136475136, 6582018229284824168619876730229402019930943462534319453394436096

Offset: 1

Author

Omar E. Pol, Dec 15 2008

Keywords

• nonn

Comments

Ultraperfect numbers (A139306), divided by 2.

Also, a(n) is the largest proper divisor of the n-th ultraperfect number.

The cototient (A051953) of the even perfect numbers (A000396). - Amiram Eldar, Mar 06 2022

These cototients are squares = (2^(p-1))^2. - Bernard Schott, Mar 14 2022

Crossrefs

Cf. A000043, A000396, A019279, A051953, A061652, A139288, A139306, A152922, A152923.

Programs

Mathematica

a[n_] := 4^(MersennePrimeExponent[n] - 1); Array[a, 12] (* Amiram Eldar, Mar 06 2022 *)

Formula

a(n) = A139306(n)/2.

a(n) = A051953(A000396(n)), if there are no odd perfect numbers. - Amiram Eldar, Mar 06 2022

a(n) = A061652(n)^2. - Bernard Schott, Mar 14 2022

Extensions

More terms from Amiram Eldar, Mar 06 2022