The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A331972 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A331972

Bi-unitary highly touchable numbers: numbers m > 1 such that a record number of numbers k have m as the sum of the proper bi-unitary divisors of k.
(history; published version)

#10 by Giovanni Resta at Tue Feb 04 03:56:50 EST 2020

STATUS

reviewed

approved

#9 by Michel Marcus at Tue Feb 04 03:16:44 EST 2020

STATUS

proposed

reviewed

#8 by Amiram Eldar at Tue Feb 04 03:07:25 EST 2020

STATUS

editing

proposed

#7 by Amiram Eldar at Tue Feb 04 03:06:37 EST 2020

LINKS

Amiram Eldar, <a href="/A331972/b331972.txt">Table of n, a(n) for n = 1..73</a> (terms below 30000)

#6 by Amiram Eldar at Mon Feb 03 23:25:01 EST 2020

LINKS

Amiram Eldar, <a href="/A331972/b331972.txt">Table of n, a(n) for n = 1..73</a>

STATUS

approved

editing

#5 by Susanna Cuyler at Mon Feb 03 22:19:09 EST 2020

STATUS

proposed

approved

#4 by Amiram Eldar at Mon Feb 03 17:08:30 EST 2020

STATUS

editing

proposed

#3 by Amiram Eldar at Mon Feb 03 07:55:27 EST 2020

CROSSREFS

Cf. A188999, A238895, A324276, A325177, A331970, A331974.

#2 by Amiram Eldar at Mon Feb 03 07:48:19 EST 2020

NAME

allocated for Amiram EldarBi-unitary highly touchable numbers: numbers m > 1 such that a record number of numbers k have m as the sum of the proper bi-unitary divisors of k.

DATA

2, 6, 8, 17, 29, 31, 55, 79, 91, 115, 121, 175, 181, 211, 295, 301, 361, 391, 421, 481, 511, 571, 631, 781, 841, 991, 1051, 1231, 1261, 1471, 1561, 1651, 1681, 1891, 2101, 2311, 2731, 3151, 3361, 3571, 3991, 4201, 4291, 4411, 4621, 5251, 5461, 6091, 6511, 6931

OFFSET

1,1

COMMENTS

The corresponding record values are 0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 14, 15, ...

The bi-unitary version of A238895.

EXAMPLE

a(1) = 2 since it is the first number which is not the sum of proper bi-unitary divisors of any number.

a(2) = 6 since it is the least number which is the sum of proper bi-unitary divisors of one number: 6 = A331970(6).

a(3) = 8 since it is the least number which is the sum of proper bi-unitary divisors of 2 numbers: 8 = A331970(10) = A331970(12).

MATHEMATICA

fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); bs[n_] := bsigma[n] - n; m = 300; v = Table[0, {m}]; Do[b = bs[k]; If[2 <= b <= m, v[[b]]++], {k, 1, m^2}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 2, m}]; s

CROSSREFS

Cf. A188999, A238895, A324276, A325177, A331970.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Feb 03 2020

STATUS

approved

editing

#1 by Amiram Eldar at Mon Feb 03 07:48:19 EST 2020

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved