A364470 a(n) is the least k > a(n-1) such that Omega(k * (a(n-1)+k)) = n, where Omega = A001222; a(1) = 1.

1, 2, 7, 11, 13, 19, 32, 56, 80, 120, 128, 224, 320, 480, 512, 896, 1280, 1920, 2048, 3584, 5120, 7680, 8192, 14336, 20480, 30720, 32768, 57344, 81920, 122880, 131072, 229376, 327680, 491520, 524288, 917504, 1310720, 1966080, 2097152, 3670016, 5242880, 7864320, 8388608, 14680064, 20971520

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

Conjecture: a(n+4) = 4*a(n) for n >= 7.

Example

a(4) = 11 as a(3) = 7 and Omega(8*(7+8)) = 5, Omega(9*(7+9)) = 6 and Omega(10*(7+10)) = 3 but Omega(11*(7+11)) = 4.

Maple

R:= 1; x:= 1;
for n from 2 to 40 do
  for y from x+1 do
    if numtheory:-bigomega(y) + numtheory:-bigomega(x+y) = n then break fi;
  od;
  R:= R, y; x:= y;
od:
R;

Crossrefs

Cf. A001222.

Sequence in context: A020583 A140557 A027697 * A235475 A146315 A038892

Adjacent sequences: A364467 A364468 A364469 * A364471 A364472 A364473

Keyword

nonn

Author

Robert Israel, Jul 25 2023

Status

approved