cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A360525 Numbers k such that A360522(k) > 2*k.

This page as a plain text file.
%I A360525 #9 Feb 11 2023 07:56:46
%S A360525 30,42,60,66,70,78,84,90,102,114,120,126,132,138,140,150,156,168,174,
%T A360525 180,186,204,210,222,228,246,252,258,276,282,294,300,318,330,348,354,
%U A360525 360,366,372,390,402,420,426,438,444,462,474,492,498,510,516,534,546,564
%N A360525 Numbers k such that A360522(k) > 2*k.
%C A360525 First differs from A308127 at n = 15.
%C A360525 Analogous to abundant numbers (A005101) with A360522 instead of A000203.
%C A360525 Subsequence of A005101 because A360522(n) <= A000203(n) for all n.
%C A360525 The least odd term is a(1698) = A360526(1) = 15015.
%C A360525 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 8, 95, 1135, 10890, 110867, 1104596, 11048123, 110534517, 1105167384, 11051009278, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1105...
%H A360525 Amiram Eldar, <a href="/A360525/b360525.txt">Table of n, a(n) for n = 1..10000</a>
%e A360525 30 is a term since A360522(30) = 72 > 2*30.
%t A360525 f[p_, e_] := p^e + e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := s[n] > 2*n; Select[Range[1000], q]
%o A360525 (PARI) is(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] + f[i,2]) > 2*n;}
%Y A360525 Cf. A000203, A308127, A360522, A360524, A360526.
%Y A360525 Subsequence of A005101.
%Y A360525 Similar sequences: A034683, A064597, A129575, A129656, A292982, A348274, A348604.
%K A360525 nonn
%O A360525 1,1
%A A360525 _Amiram Eldar_, Feb 10 2023