A378912 Irregular triangle read by rows: row n lists all positive m such that sigma(m) divides n, where sigma is the sum-of-divisors function (A000203).
1, 1, 1, 2, 1, 3, 1, 1, 2, 5, 1, 4, 1, 3, 7, 1, 2, 1, 1, 1, 2, 3, 5, 6, 11, 1, 9, 1, 4, 13, 1, 2, 8, 1, 3, 7, 1, 1, 2, 5, 10, 17, 1, 1, 3, 19, 1, 2, 4, 1, 1, 1, 2, 3, 5, 6, 7, 11, 14, 15, 23, 1, 1, 9, 1, 2, 1, 3, 4, 12, 13, 1, 1, 2, 5, 8, 29, 1, 16, 25, 1, 3, 7, 21, 31
Offset: 1
Examples
Triangle begins: n\k| 1 2 3 4 5 6 ... ------------------------------- 1 | 1; 2 | 1; 3 | 1, 2; 4 | 1, 3; 5 | 1; 6 | 1, 2, 5; 7 | 1, 4; 8 | 1, 3, 7; 9 | 1, 2; 10 | 1; 11 | 1; 12 | 1, 2, 3, 5, 6, 11; 13 | 1, 9; 14 | 1, 4, 13; 15 | 1, 2, 8; 16 | 1, 3, 7; 17 | 1; 18 | 1, 2, 5, 10, 17; 19 | 1; 20 | 1, 3, 19; ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10634 (rows 1..2000 of triangle, flattened).
- Index entries for sequences related to sigma(n)
Programs
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Mathematica
With[{nmax = 50}, Table[PositionIndex[Divisible[n, #[[;; n]]]][True], {n, nmax}] & [DivisorSigma[1, Range[nmax]]]] -
PARI
row(n) = select(x->(!(n % sigma(x))), [1..n]); \\ Michel Marcus, Dec 11 2024
Formula
T(n,k) <= n (see A319068).