This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Divisors[4064] (* Paolo Xausa, Jul 22 2024 *)
divisors(4064) \\ Charles R Greathouse IV, Jun 21 2017
Divisors[16775168] (* Wesley Ivan Hurt, Mar 20 2022 *)
divisors(16775168) \\ Charles R Greathouse IV, Jun 22 2017
The structure of divisors of 4064 (see A138814) ................................................................. n ........... Divisor . Formula ....... Divisor written in base 2 ................................................................. 1) ................ 1 = 2^0 ........... 1 2) ................ 2 = 2^1 ........... 10 3) ................ 4 = 2^2 ........... 100 4) ................ 8 = 2^3 ........... 1000 5) ............... 16 = 2^4 ........... 10000 6) A134708(4) = .. 32 = 2^5 ........... 100000 7) A000668(4) = . 127 = 2^7 - 2^0 ..... 1111111 8) .............. 254 = 2^8 - 2^1 ..... 11111110 9) .............. 508 = 2^9 - 2^2 ..... 111111100 10) ............ 1016 = 2^10- 2^3 ..... 1111111000 11) ............ 2032 = 2^11- 2^4 ..... 11111110000 12) A133028(4) = 4064 = 2^12- 2^5 ..... 111111100000
FromDigits/@(IntegerDigits[#,2]&/@Divisors[4064]) (* Harvey P. Dale, Oct 12 2016 *)
The structure of divisors of 16775168 (see A138815) ..................................................................... n ............... Divisor . Formula ....... Divisor written in base 2 ..................................................................... 1) .................... 1 = 2^0 ........... 1 2) .................... 2 = 2^1 ........... 10 3) .................... 4 = 2^2 ........... 100 4) .................... 8 = 2^3 ........... 1000 5) ................... 16 = 2^4 ........... 10000 6) ................... 32 = 2^5 ........... 100000 7) ................... 64 = 2^6 ........... 1000000 8) .................. 128 = 2^7 ........... 10000000 9) .................. 256 = 2^8 ........... 100000000 10) ................. 512 = 2^9 ........... 1000000000 11) ................ 1024 = 2^10 .......... 10000000000 12) A134708(5) = ... 2048 = 2^11 .......... 100000000000 13) A000668(5) = ... 8191 = 2^13 - 2^0 .... 1111111111111 14) ............... 16382 = 2^14 - 2^1 .... 11111111111110 15) ............... 32764 = 2^15 - 2^2 .... 111111111111100 16) ............... 65528 = 2^16 - 2^3 .... 1111111111111000 17) .............. 131056 = 2^17 - 2^4 .... 11111111111110000 18) .............. 262112 = 2^18 - 2^5 .... 111111111111100000 19) .............. 524224 = 2^19 - 2^6 .... 1111111111111000000 20) ............. 1048448 = 2^20 - 2^7 .... 11111111111110000000 21) ............. 2096896 = 2^21 - 2^8 .... 111111111111100000000 22) ............. 4193792 = 2^22 - 2^9 .... 1111111111111000000000 23) ............. 8387584 = 2^23 - 2^10 ... 11111111111110000000000 24) A133028(5) = 16775168 = 2^24 - 2^11 ... 111111111111100000000000
FromDigits[IntegerDigits[#,2]]&/@Divisors[16775168] (* Harvey P. Dale, May 26 2015 *)
a(3)=247 because the 3rd perfect number is 496 and 496/2 is 248. a(3)=248-1.
p = Select[2^Range[400] - 1, PrimeQ]; p*(p+1)/4 - 1 (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
a(3)=61 because the 3rd perfect number is 496 and 2^3=8 and (496/8)-1=61.
The structure of divisors of 248 (see A018355) .................................................................. n ............ Divisor . Formula ....... Divisor written in base 2 .................................................................. 1) ................. 1 = 2^0 ........... 1 2) ................. 2 = 2^1 ........... 10 3) ................. 4 = 2^2 ........... 100 4) A134708(3) = .... 8 = 2^3 ........... 1000 5) A000668(3) = ... 31 = 2^5 - 2^0 ..... 11111 6) ................ 62 = 2^6 - 2^1 ..... 111110 7) ............... 124 = 2^7 - 2^2 ..... 1111100 8) A133028(3) = .. 248 = 2^8 - 2^3 ..... 11111000
FromDigits[IntegerDigits[#,2]]&/@Divisors[248] (* Harvey P. Dale, Apr 01 2017 *)
divisors(248) \\ Charles R Greathouse IV, Sep 06 2016
Accumulate[(# (#+1))/2&/@Select[2^Range[90]-1,PrimeQ] ]/2 (* Harvey P. Dale, Sep 04 2014 *)
Comments