A362404 Numbers k such that k and k+1 are both in A362401.

24, 27, 48, 79, 120, 168, 199, 288, 350, 360, 378, 391, 447, 507, 528, 775, 840, 895, 960, 1088, 1136, 1368, 1638, 1639, 1680, 1848, 1849, 2095, 2127, 2208, 2322, 2749, 2808, 3720, 3726, 3798, 3799, 3919, 4050, 4087, 4488, 4550, 4872, 5040, 5328, 5448, 5631, 6240

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..3557 (terms below 10^8)

Example

24 is a term since 24 and 25 are both in the range of A162296: A162296(20) = 24 and A162296(25) = 25.

Mathematica

s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1)]; s[1] = 0; seq[max_] := Module[{v = Select[Union[Array[s, max]], 0 < # <= max &], i}, i = Position[Differences[v], 1] // Flatten; v[[i]]]; seq[10^4]

Prog

(PARI) s(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((p^(e + 1) - 1)/(p - 1))) -  prod(i = 1, #f~, f[i, 1] + 1); }
lista(kmax) = {my(v = select(x -> (x < kmax), Set(vector(kmax, k, s(k))))); for(k=1, #v-1, if(v[k+1] - v[k] == 1, print1(v[k], ", "))); }

Crossrefs

Subsequence of A362401.

A362405 is a subsequence.

Cf. A162296.

Sequence in context: A162465 A067193 A095235 * A316725 A164778 A268540

Adjacent sequences: A362401 A362402 A362403 * A362405 A362406 A362407

Keyword

nonn

Author

Amiram Eldar, Apr 18 2023

Status

approved