A355433 Numbers k such that k is sqrt(k)-smooth and k+1 is sqrt(k+1)-smooth.

8, 24, 48, 49, 63, 80, 120, 125, 168, 175, 195, 224, 242, 288, 324, 350, 351, 360, 363, 374, 384, 399, 440, 441, 455, 475, 494, 512, 528, 539, 560, 575, 594, 624, 675, 714, 728, 735, 759, 832, 840, 874, 896, 935, 960, 968, 1000, 1014, 1023, 1044, 1053, 1088, 1104

Offset

1,1

Comments

Numbers k such that k and k+1 are both in A048098.

This sequence is infinite: if p is an odd prime then p^2-1 is a term.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

8 is a term since 8 is sqrt(8)-smooth (2^2 <= 8) and 9 is sqrt(9)-smooth (3^2 <= 9).

Mathematica

smQ[n_] := FactorInteger[n][[-1, 1]]^2 <= n; Select[Range[1000], smQ[#] && smQ[# + 1] &]

Crossrefs

Cf. A048098, A355434.

Subsequences: A084920 \ {3}, A060355, A348119.

Sequence in context: A152531 A074348 A063403 * A348119 A306415 A122812

Adjacent sequences: A355430 A355431 A355432 * A355434 A355435 A355436

Keyword

nonn

Author

Amiram Eldar, Jul 02 2022

Status

approved