A326065
Sum of divisors of the largest proper divisor of n: a(n) = sigma(A032742(n)).
Original entry on oeis.org
1, 1, 1, 3, 1, 4, 1, 7, 4, 6, 1, 12, 1, 8, 6, 15, 1, 13, 1, 18, 8, 12, 1, 28, 6, 14, 13, 24, 1, 24, 1, 31, 12, 18, 8, 39, 1, 20, 14, 42, 1, 32, 1, 36, 24, 24, 1, 60, 8, 31, 18, 42, 1, 40, 12, 56, 20, 30, 1, 72, 1, 32, 32, 63, 14, 48, 1, 54, 24, 48, 1, 91, 1, 38, 31, 60, 12, 56, 1, 90, 40, 42, 1, 96, 18, 44, 30, 84, 1, 78, 14
Offset: 1
Cf.
A000203,
A013661,
A020639,
A032742,
A067029,
A143112,
A326066,
A326067,
A326068,
A326069,
A326135.
A143111
Triangle read by rows, T(n,k) = largest proper divisor of A127093(n,k) where (largest proper divisor)(n) = A032742(n) if n>0 and 0 if n=0.
Original entry on oeis.org
1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 4, 1, 0, 1, 0, 0, 0, 0, 0, 3, 1, 1, 0, 0, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 3, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 7
Offset: 1
First few rows of the triangle:
1;
1, 1;
1, 0, 1;
1, 1, 0, 2;
1, 0, 0, 0, 1;
1, 1, 1, 0, 0, 3;
1, 0, 0, 0, 0, 0, 1;
1, 1, 0, 2, 0, 0, 0, 4;
1, 0, 1, 0, 0, 0, 0, 0, 3;
1, 1, 0, 0, 1, 0, 0, 0, 0, 5;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1, 1, 1, 2, 0, 3, 0, 0, 0, 0, 0, 6;
...
Example: The divisors of 12 are shown in row 12 of triangle A127093:
(1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12);
and the largest proper divisors of those terms are:
(1, 1, 1, 2, 0, 3, 0, 0, 0, 0, 0, 6)
where the first 12 terms of A031742 (largest proper divisors of n) are:
(1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6).
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Table[If[# > 1, Divisors[#][[-2]], #] &[k*Boole[Divisible[n, k]]], {n, 14}, {k, n}] (* Michael De Vlieger, Dec 19 2022 *)
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t(n,k) = k * 0^(n % k); \\ A127093
f(n) = if(n<=1, n, n/factor(n)[1, 1]); \\ A032742
T(n,k) = f(t(n,k));
row(n) = vector(n, k, T(n,k)); \\ Michel Marcus, Dec 19 2022
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T1(n,k) = 0^(n % k); \\ A051731
a2(n) = if(n==1, 1, n/factor(n)[1, 1]); \\ A032742
tabl(nn) = my(m1 = matrix(nn,nn,n,k,T1(n,k)), v2 = vector(nn,n,a2(n))); m1*matdiagonal(v2); \\ Michel Marcus, Dec 19 2022
Typo in data corrected and new name from existing formula by
Michel Marcus, Dec 19 2022
Showing 1-2 of 2 results.
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