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 A135653 Divisors of 496 (the 3rd perfect number), written in base 2. 11
 1, 10, 100, 1000, 10000, 11111, 111110, 1111100, 11111000, 111110000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of divisors of the third perfect number is equal to 2*A000043(3)=A061645(3)=10. LINKS FORMULA a(n)=A018487(n), written in base 2. Also, for n=1 .. 10: If n<=(A000043(3)=5) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(3)=5 digits "1" and (n-1-A000043(3)) digits "0". EXAMPLE The structure of divisors of 496 (see A018487) ------------------------------------------------------------------------- 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 ... (The 3rd superperfect number) 6)........ 31 = 2^5 - 2^0 ..... 11111 ... (The 3rd Mersenne prime) 7)........ 62 = 2^6 - 2^1 ..... 111110 8)....... 124 = 2^7 - 2^2 ..... 1111100 9)....... 248 = 2^8 - 2^3 ..... 11111000 10)...... 496 = 2^9 - 2^4 ..... 111110000 ... (The 3rd perfect number) MATHEMATICA FromDigits[IntegerDigits[#, 2]]&/@Divisors[496] (* Harvey P. Dale, Dec 02 2018 *) PROG (PARI) apply(n->fromdigits(binary(n)), divisors(496)) \\ Charles R Greathouse IV, Jun 21 2017 CROSSREFS For more information see A018487 (Divisors of 496). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652. Sequence in context: A136866 A136878 A136871 * A219111 A232659 A232660 Adjacent sequences:  A135650 A135651 A135652 * A135654 A135655 A135656 KEYWORD base,nonn,fini,full,easy,less AUTHOR Omar E. Pol, Feb 23 2008, Mar 03 2008 STATUS approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)