A333951 -id:A333951 - cp's OEIS frontend

A357608 Numbers k such that k and k+1 are both in A357605.

76544, 104895, 126224, 165375, 170624, 174824, 201824, 245024, 257984, 271215, 273104, 316575, 338624, 387855, 447615, 469664, 477224, 540224, 618975, 633555, 641024, 659295, 705375, 752895, 770175, 842624, 843975, 862784, 870975, 893024, 913275, 957824, 1047375

Offset: 1

Amiram Eldar, Oct 06 2022

nonn

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

			76544 is a term since 76544 and 76545 are both in A357605: A162296(76544) = 170688 > 2*76544 and A162296(76545) = 157248 > 2*76545.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A162296.
Subsequence of A013929, A096399 and A357605.
Similar sequences: A096399, A283418, A318167, A327635, A327942, A331412, A333951.

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]; Select[Range[2, 10^6], q[#] && q[#+1] &]

A339937 Numbers k such that k and k+1 are both coreful abundant numbers (A308053).

Original entry on oeis.org

2282175, 33350624, 46734975, 86424975, 87152624, 105674624, 126114975, 169707824, 179762624, 214491375, 221370975, 235857824, 266022224, 270586575, 278524575, 297774224, 360021375, 372683024, 380858624, 395715375, 425840624, 470624175, 489873824, 503963775

Offset: 1

Amiram Eldar, Dec 23 2020

nonn

			2282175 is a term since 2282175 and 2282176 are both coreful abundant numbers.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Subsequence of A308053.

Similar sequences: A096399, A283418, A318167, A327635, A327942, A330872, A331412, A333951.

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); abQ[n_] := s[n] > 2*n; q1 = False; seq = {}; Do[q2 = abQ[n]; If[q1 && q2, AppendTo[seq, n - 1]]; q1 = q2, {n, 2, 10^8}]; seq

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, ", "))));

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A357608 Numbers k such that k and k+1 are both in A357605.

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A339937 Numbers k such that k and k+1 are both coreful abundant numbers (A308053).

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

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