A110875 -id:A110875 - cp's OEIS frontend

A109322 a(n) is the minimum positive integer j such that [j, j+n-1] does not contain any values of sigma(k) (i.e., sum of all positive divisors of k).

2, 9, 9, 49, 49, 423, 423, 423, 423, 1333, 1333, 4425, 4425, 4425, 4425, 8763, 8763, 14089, 14089, 22825, 22825, 22825, 22825, 40291, 40291, 40291, 40291, 40291, 40291, 178705, 178705, 661285, 661285, 661285, 661285, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141

Offset: 1

Max Alekseyev and Jud McCranie, Aug 08 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..85 (terms < 10^10)
Art of Problem Solving, Gaps in {sigma(n)}...

Cf. A002191, A083531, A109323, A109324, A110875.

A109323 A109322 with duplicates removed.

Original entry on oeis.org

2, 9, 49, 423, 1333, 4425, 8763, 14089, 22825, 40291, 178705, 661285, 4543141, 20706715, 29243521, 31089603, 32341621, 99158905, 417976441, 1186496401, 1540962199, 2097064537, 8602909969

Offset: 1

Max Alekseyev and Jud McCranie, Aug 08 2005

Cf. A109322, A109324, A110875.

a(20)-a(23) from Donovan Johnson, Jan 25 2012

A109324 Gap lengths associated with A109323.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 17, 19, 23, 29, 31, 35, 47, 53, 55, 57, 59, 67, 71, 73, 81, 83, 85

Offset: 1

Max Alekseyev and Jud McCranie, Aug 08 2005

Cf. A109322, A109323, A110875.

a(19)-a(23) from Donovan Johnson, Jan 25 2012

A231965 Smallest integer starting a group of exactly n consecutive untouchable numbers (A005114) with term differences of 2.

Original entry on oeis.org

246, 288, 892, 9020, 11456, 23480, 52274, 33686, 190070, 1741856, 1668564, 7806762

Offset: 2

Michel Marcus, Nov 16 2013

Such n-tuplets from A005114 correspond to n+1 positive numbers interspersed with n zeros in A070015, and starting at a(n) - 1. For instance, a(4) = 892 is related to A070015(891) and consecutive values: 2661, 0, 4147, 0, 2945, 0, 1287, 0, 9757.

			a(5) = 9020, because 9020, 9022, 9024, 9026, 9028 are untouchable, while 9018 and 9030 are not so (A001065). For examples with smaller n, see A231964 comments.

Eric Weisstein's World of Mathematics, Untouchable Number.
Wikipedia, Untouchable number

Cf. A001065, A005114, A231964.

Cf. A110875 (analog for sigma(n)).

oksucc(v, vi, n) = {for (i = 1, n-1, if (! vecsearch(v, vi+2*i, ) , return (0));); return(! vecsearch(v, vi-2) && !vecsearch(v, vi+2*n));}
a(n) = {v = readvec("untouchable.log"); for (i=1, #v, vi = v[i]; if (oksucc(v, vi, n), return(vi)););} \\ readvec reads the file obtained by keeping the second column of b005114.txt seen as a csv file.

a(10)-a(13) from Donovan Johnson, Nov 16 2013

Definition, data, and Pari script corrected by Michel Marcus with Donovan Johnson, Nov 18 2013

cp's OEIS Frontend

A109322 a(n) is the minimum positive integer j such that [j, j+n-1] does not contain any values of sigma(k) (i.e., sum of all positive divisors of k).

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A109323 A109322 with duplicates removed.

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A109324 Gap lengths associated with A109323.

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A231965 Smallest integer starting a group of exactly n consecutive untouchable numbers (A005114) with term differences of 2.

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