A307746
Triangle read by rows, obtained by omitting all the 1's from the triangle in A307641 (except for the first row).
Original entry on oeis.org
1, 2, 3, 2, 2, 5, 2, 3, 7, 2, 2, 2, 3, 3, 2, 5, 11, 2, 3, 2, 13, 2, 7, 3, 5, 2, 2, 2, 2, 17, 2, 3, 3, 19, 2, 2, 5, 3, 7, 2, 11, 23, 2, 3, 2, 2, 5, 5, 2, 13, 3, 3, 3, 2, 2, 7, 29, 2, 3, 5, 31, 2, 2, 2, 2, 2, 3, 11, 2, 17, 5, 7, 2, 3, 2, 3, 37, 2, 19, 3, 13
Offset: 1
Triangle begins:
1;
2;
3;
2, 2;
5;
2, 3;
7;
2, 2, 2;
3, 3;
2, 5;
11;
2, 3, 2;
...
-
f(n)=ispower(n, , &n); if(isprime(n), n, 1); \\ A014963
row(n) = if (n==1, [1], my(d=divisors(n)); select(x->x!=1, vector(#d, k, f(d[k]))));
tabl(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Apr 27 2019
A088387
Prime corresponding to largest prime power factor of n, a(1)=1.
Original entry on oeis.org
1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 2, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 2, 41, 7, 43, 11, 3, 23, 47, 2, 7, 5, 17, 13, 53, 3, 11, 2, 19, 29, 59, 5, 61, 31, 3, 2, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19, 11, 13, 79, 2, 3, 41, 83, 7, 17
Offset: 1
a(6) = a(2*3) = 3 because 3^1 > 2^1;
a(36) = a((2^2)(3^2)) = 3 because 3^2 > 2^2;
a(12) = a((2^2)*3) = 2 because 2^2 > 3^1.
-
f[n_] := Sort[ {#[[1]]^#[[2]], #[[1]]} & /@ FactorInteger@ n][[ -1, 2]]; Array[f, 85] (* Robert G. Wilson v, Nov 05 2007 *)
a[n_] := MaximalBy[FactorInteger[n], Power @@ # &][[1, 1]];
Array[a, 85] (* Jean-François Alcover, Jun 27 2019 *)
-
A088387(n) = if(1==n,1,my(f=factor(n),p=0); isprimepower(vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2])),&p); (p)); \\ Antti Karttunen, Jul 22 2018
-
from sympy import factorint
def A088387(n): return max(((p**e,p) for p, e in factorint(n).items()), default=(0,1))[1] # Chai Wah Wu, Apr 17 2023
A307662
Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.
Original entry on oeis.org
1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 1, 1, 8, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 2, 1, 1, 5, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 2, 3, 4, 1, 6, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13
Offset: 1
Triangle begins:
1,
1, 2,
1, 1, 3,
1, 2, 1, 4,
1, 1, 1, 1, 5,
1, 2, 3, 1, 1, 6,
1, 1, 1, 1, 1, 1, 7,
1, 2, 1, 4, 1, 1, 1, 8,
1, 1, 3, 1, 1, 1, 1, 1, 9,
1, 2, 1, 1, 5, 1, 1, 1, 1,10,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,11,
1, 2, 3, 4, 1, 6, 1, 1, 1, 1, 1,12,
...
-
Table[Map[If[Mod[n, #] == 0, #, 1] &, Range@ n], {n, 13}] // Flatten (* Michael De Vlieger, Apr 23 2019 *)
-
row(n) = vector(n, k, if ((n % k) == 0, k, 1)); \\ Michel Marcus, Apr 21 2019
A307723
Naturally ordered prime factorization of n as a quasi-logarithmic word over the binary alphabet {1,0}.
Original entry on oeis.org
10, 1100, 1010, 110100, 101100, 11011000, 101010, 11001100, 10110100, 1101101000, 10110010, 1101100100, 1011011000, 1100110100, 10101010, 1101010100, 1011001100, 110110011000, 1010110100, 110011011000
Offset: 2
The sequence begins:
n a(n)
-- -----------
1
2 10
3 1100
4 1010
5 110100
6 101100
7 11011000
8 101010
9 11001100
10 10110100
11 1101101000
12 10110010
...
Showing 1-4 of 4 results.
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