A079665 Triangular array read by rows: row s contains integers of the form (2^s+1)/(2^r+1) in order of increasing r <= s-1.

3, 11, 13, 43, 171, 57, 205, 683, 241, 2731, 3277, 10923, 3641, 993, 43691, 52429, 4033, 174763, 61681, 699051, 233017, 16257, 838861, 2796203, 65281, 11184811, 1016801, 13421773, 44739243, 14913081, 261633, 15790321, 178956971, 214748365

Offset

1,1

Comments

Conjecture: (b^s+1)/(b^r+1) is an integer if and only if: 1) r<s/2, 2) if s==1 (mod 2) then r is divisor of s, 3) if s=k*2^t with gcd(k,2^t)=1 then r is 2^t*u with u dividing k

Links

Table of n, a(n) for n=1..34.

Example

s=2: no terms
s=3: 3
s=4: no terms
s=5: 11
s=6: 13
s=7: 43
s=8: no terms
s=9: 171, 57
...

Prog

(PARI) for(x=2, 30, for(y=1, x-1, if(Mod(2^x+1, 2^y+1), 0, print1((2^x+1)\(2^y+1)", "))))

Crossrefs

Cf. A079672, A079581, A079673, A370425.

Sequence in context: A113049 A370425 A225097 * A281728 A083992 A370488

Adjacent sequences: A079662 A079663 A079664 * A079666 A079667 A079668

Keyword

nonn,tabf

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 25 2003

Extensions

Definition corrected by Max Alekseyev, Feb 18 2024

Status

approved