login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197594 Sum of the cubes of the first odd numbers up to a(n) equals the n-th perfect number. 1
3, 7, 15, 127, 511, 1023, 65535, 2147483647, 35184372088831, 18014398509481983, 18446744073709551615, 3705346855594118253554271520278013051304639509300498049262642688253220148477951 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Except for the first perfect number 6, every even perfect number 2^(p-1)*(2^p - 1) is the sum of the cubes of the first 2^((p-1)/2) odd numbers.
REFERENCES
Albert H. Beiler: Recreations in the theory of numbers, New York, Dover, Second Edition, 1966, p. 22.
LINKS
FORMULA
(1/8)*(a(n) + 1)^2*(a(n)^2 + 2*a(n) - 1) = 2^(p-1)*(2^p - 1) with p = 2*log(a(n) + 1)/log(2) - 1 a Mersenne prime.
a(n) = 2^((A000043(n)+1)/2) - 1. - Charles R Greathouse IV, Oct 17 2011
a(n) = sqrt(1 + sqrt(8*A000396(n) + 1)) - 1. - Martin Renner, Oct 17 2011
a(n) = 2^A138576(n) - 1. - César Aguilera, Apr 20 2024
a(n) = sqrt(2*(A000668(n)+1))-1 for n > 1. - César Aguilera, May 21 2024
EXAMPLE
a(2)=3, since 1^3 + 3^3 = 28, which is the second perfect number.
a(3)=7, since 1^3 + 3^3 + 5^3 + 7^3 = 496, which is the third perfect number.
CROSSREFS
Sequence in context: A193831 A246719 A077775 * A206851 A033089 A370661
KEYWORD
nonn
AUTHOR
Martin Renner, Oct 16 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)