A378638 Irregular triangle read by rows: row n lists all m such that phi(m) divides n, where phi is the Euler totient function (A000010).
1, 2, 1, 2, 3, 4, 6, 1, 2, 1, 2, 3, 4, 5, 6, 8, 10, 12, 1, 2, 1, 2, 3, 4, 6, 7, 9, 14, 18, 1, 2, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 1, 2, 1, 2, 3, 4, 6, 11, 22, 1, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 18, 21, 26, 28, 36, 42, 1, 2, 1, 2, 3, 4, 6, 1, 2
Offset: 1
Examples
Triangle begins: n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... ---------------------------------------------------------------------------------- 1 | 1, 2; 2 | 1, 2, 3, 4, 6; 3 | 1, 2; 4 | 1, 2, 3, 4, 5, 6, 8, 10, 12; 5 | 1, 2; 6 | 1, 2, 3, 4, 6, 7, 9, 14, 18; 7 | 1, 2; 8 | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30; 9 | 1, 2; 10 | 1, 2, 3, 4, 6, 11, 22; 11 | 1, 2; 12 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 18, 21, 26, 28, 36, 42; 13 | 1, 2; 14 | 1, 2, 3, 4, 6; 15 | 1, 2; 16 | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 60; 17 | 1, 2; 18 | 1, 2, 3, 4, 6, 7, 9, 14, 18, 19, 27, 38, 54; 19 | 1, 2; 20 | 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 22, 25, 33, 44, 50, 66; ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..13988 (rows 1..1000 of triangle, flattened).
Crossrefs
Programs
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Mathematica
With[{nmax = 25}, Table[If[OddQ[n], {1, 2}, PositionIndex[Divisible[n, #[[;; Max[n^2, 6]]]]][True]], {n, nmax}] & [EulerPhi[Range[nmax^2]]]] -
PARI
row(n) = select(x->!(n % eulerphi(x)), [1..max(n^2, 6)]); \\ Michel Marcus, Dec 05 2024
Formula
T(n,k) <= n^2, for n > 2 (see A319048).
Comments