The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A357685 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A357685

Numbers k such that A293228(k) > k.
(history; published version)

#10 by Alois P. Heinz at Wed Oct 12 04:34:49 EDT 2022

STATUS

reviewed

approved

#9 by Michel Marcus at Wed Oct 12 02:19:32 EDT 2022

STATUS

proposed

reviewed

#8 by Amiram Eldar at Wed Oct 12 02:05:49 EDT 2022

STATUS

editing

proposed

#7 by Amiram Eldar at Wed Oct 12 01:56:04 EDT 2022

LINKS

Amiram Eldar, <a href="/A357685/b357685.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#6 by Michael De Vlieger at Sun Oct 09 12:05:22 EDT 2022

STATUS

reviewed

approved

#5 by Joerg Arndt at Sun Oct 09 10:10:22 EDT 2022

STATUS

proposed

reviewed

#4 by Amiram Eldar at Sun Oct 09 10:09:14 EDT 2022

STATUS

editing

proposed

#3 by Amiram Eldar at Sun Oct 09 09:41:42 EDT 2022

NAME

allocated for Amiram EldarNumbers k such that A293228(k) > k.

DATA

30, 42, 60, 66, 70, 78, 84, 102, 114, 132, 138, 140, 156, 174, 186, 204, 210, 222, 228, 246, 258, 276, 282, 318, 330, 348, 354, 366, 372, 390, 402, 420, 426, 438, 444, 462, 474, 492, 498, 510, 516, 534, 546, 564, 570, 582, 606, 618, 636, 642, 654, 660, 678, 690

OFFSET

1,1

COMMENTS

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 7, 79, 843, 8230, 83005, 826875, 8275895, 82790525, 827718858, 8276571394, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0827... .

EXAMPLE

30 is a term since its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15} and their sum is 42 > 30.

60 is a term since its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15, 30} and their sum is 72 > 60.

MATHEMATICA

s[n_] := Times @@ (1 + (f = FactorInteger[n])[[;; , 1]]) - If[AllTrue[f[[;; , 2]], # == 1 &], n, 0]; Select[Range[2, 1000], s[#] > # &]

PROG

(PARI) is(n) = {my(f = factor(n), s); s = prod(i=1, #f~, f[i, 1]+1); if(n==1 || vecmax(f[, 2]) == 1, s -= n); s > n};

CROSSREFS

Cf. A005117, A293228.

Disjoint union of A087248 and A357686.

Subsequence of A005101.

Similar sequences: A034683, A064597, A129575, A129656, A292982, A348274, A348604.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Oct 09 2022

STATUS

approved

editing

#2 by Amiram Eldar at Sun Oct 09 09:39:34 EDT 2022

KEYWORD

allocating

allocated

#1 by Amiram Eldar at Sun Oct 09 09:39:34 EDT 2022

NAME

allocated for Amiram Eldar

KEYWORD

allocating

STATUS

approved