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A362405
Numbers k such that k, k+1 and k+2 are all in A362401.
2
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 18 2023
STATUS
approved