A275164 The 167 numbers n such that n(n+1) is 19-smooth.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 32, 33, 34, 35, 38, 39, 44, 48, 49, 50, 51, 54, 55, 56, 63, 64, 65, 75, 76, 77, 80, 84, 90, 95, 98, 99, 104, 119, 120, 125, 132, 135, 143, 152, 153, 168, 169, 170, 175, 189, 195, 208, 209, 220, 224, 242, 255, 272, 285, 288, 323, 324, 342, 350, 351, 360, 363, 374, 384, 399, 440

Offset

1,2

Comments

See A002071.

The full list of 167 terms is given in the b-file (this is the 8th row of the table A138180).

Links

Jean-François Alcover, Table of n, a(n) for n = 1..167

Mathematica

pMax = 19; smoothMax = 10^15; smoothNumbers[p_?PrimeQ, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand@Log[pp[[j]], max/Times @@ (Take[pp, j - 1]^Take[aa, j - 1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; Select[(Sqrt[1 + 4*smoothNumbers[pMax, smoothMax]] - 1)/2, IntegerQ]

Crossrefs

Cf. A002071, A145604, A138180, A145605, A002072, A085152, A085153, A252493, A252492,A275156.

Sequence in context: A276181 A171829 A162421 * A076499 A092629 A246101

Adjacent sequences: A275161 A275162 A275163 * A275165 A275166 A275167

Keyword

fini,full,nonn

Author

Jean-François Alcover, Nov 14 2016

Status

approved