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

Author

Amiram Eldar, Apr 18 2023

Keywords

• nonn

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?

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A362401 and A362404.

Cf. A162296.

Programs

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]

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], ", ")));}