A357608 -id:A357608 - cp's OEIS frontend

A357609 Numbers k such that k, k+1, and k+2 are all in A357605.

10667829248, 14322877568, 25929352448, 26967189248, 31315096448, 32186016224, 35337613310, 36312573374, 41326711424, 53162460350, 69405075584, 71840196350, 72806666750, 73217757248, 83103523424, 106184935934, 109302242048, 111640866974, 115294917374, 116768901248

Offset: 1

Amiram Eldar, Oct 06 2022

nonn

Numbers k such that A162296(k) > 2*k, A162296(k+1) > 2*(k+1), and A162296(k+2) > 2*(k+2).

			10667829248 is a term since 10667829248, 10667829249 and 10667829250 are all in A357605: A162296(10667829248) = 21342038784 > 2*10667829248, A162296(10667829249) = 21798236160 > 2*10667829249 and A162296(10667829250) = 21810824640 > 2*10667829250.

Amiram Eldar, Table of n, a(n) for n = 1..209 (terms below 10^12)

Cf. A162296.

Subsequence of A013929, A096536, A357605 and A357608.

q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) > 2*n]; v = Cases[Import["https://oeis.org/A096536/b096536.txt", "Table"], {, }][[;; , 2]]; s = {}; Do[n = v[[k]]; If[q[n] && q[n+1] && q[n+2], AppendTo[s, n]], {k, 1, Length[v]}]; s

A380933 Numbers k such that k and k+1 are both in A380929.

Original entry on oeis.org

121643775, 157390064, 161019495, 275734304, 584899875, 1493214975, 1614323655, 2043708975, 3081783375, 3118599224, 3426851295, 3902652495, 3947893424, 5849043375, 11731509855, 12138531615, 13008843224, 14598032624, 17588484584, 19782621495, 20191564575, 20759209064

Offset: 1

Amiram Eldar, Feb 08 2025

Numbers k such that A380845(k) > 2*k and A380845(k+1) > 2*(k+1).

			121643775 is a term since A380845(121643775) = 244722015 > 2 * 121643775 = 243287550, and A380845(121643776) = 256456081 > 2 * 121643776 = 243287552.

Amiram Eldar, Table of n, a(n) for n = 1..32

Subsequence of A096399 and A380929.
Cf. A380845, A380932.
Similar sequences: A283418, A318167, A327635, A327942, A331412, A333951, A357608, A364727, A364861.

q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] > 2*k];
seq[lim_] := Module[{s = {}}, Do[If[q[k], If[q[k-1], AppendTo[s, k-1]]; If[q[k+1], AppendTo[s, k]]], {k, 3, lim, 2}]; s];
seq[3*10^8]

isab(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) > 2*k;}
list(lim) = forstep(k = 3, lim, 2, if(isab(k), if(isab(k-1), print1(k-1, ", ")); if(isab(k+1), print1(k, ", "))));

cp's OEIS Frontend

A357609 Numbers k such that k, k+1, and k+2 are all in A357605.

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