A362405 Numbers k such that k, k+1 and k+2 are all in A362401.

1638, 1848, 3798, 11448, 16854, 26910, 35574, 37248, 57120, 69678, 69822, 85848, 94248, 110526, 208848, 272214, 305046, 310248, 335478, 335479, 368448, 573048, 580680, 687240, 1017126, 1154270, 1230606, 1289358, 1423248, 1467414, 1697808, 1718880, 1776750, 1777248

Offset

1,1

Comments

Up to 10^8, k = 335478 is the only number k such that k, k+1, k+2 and k+3 are all in A362401. Are there any other such terms?

Links

Amiram Eldar, Table of n, a(n) for n = 1..132 (terms below 10^8)

Example

1638 is a term since 1638, 1639 and 1640 are all in the range of A162296: A162296(1053) = 1638, A162296(576) = 1639 and A162296(1636) = 1640.

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 &], w, i, j}, i = Position[Differences[v], 1] // Flatten; w = v[[i]]; j = Position[Differences[w], 1] // Flatten; w[[j]]]; seq[10^6]

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-2, if(v[k+1] - v[k] == 1 && v[k+2] - v[k+1] == 1, print1(v[k], ", "))); }

Crossrefs

Subsequence of A362401 and A362404.

Cf. A162296.

Sequence in context: A054808 A218010 A298075 * A239160 A206234 A158775

Adjacent sequences: A362402 A362403 A362404 * A362406 A362407 A362408

Keyword

nonn

Author

Amiram Eldar, Apr 18 2023

Status

approved