A339496 T(n, k) = Sum(divisors(k) union {k*j : j = 2..floor(n/k)}). Triangle read by rows.

1, 3, 3, 6, 3, 4, 10, 7, 4, 7, 15, 7, 4, 7, 6, 21, 13, 10, 7, 6, 12, 28, 13, 10, 7, 6, 12, 8, 36, 21, 10, 15, 6, 12, 8, 15, 45, 21, 19, 15, 6, 12, 8, 15, 13, 55, 31, 19, 15, 16, 12, 8, 15, 13, 18, 66, 31, 19, 15, 16, 12, 8, 15, 13, 18, 12, 78, 43, 31, 27, 16, 24, 8, 15, 13, 18, 12, 28

Offset

1,2

Comments

For the connection with paths in the divisor graph of {1,...,n} see the comment in A339492.

Links

Table of n, a(n) for n=1..78.

Example

The triangle starts:
[1]                       1;
[2]                      3, 3;
[3]                    6, 3, 4;
[4]                  10, 7, 4, 7;
[5]                15, 7, 4, 7, 6;
[6]              21, 13, 10, 7, 6, 12;
[7]            28, 13, 10, 7, 6, 12, 8;
[8]          36, 21, 10, 15, 6, 12, 8, 15;
[9]        45, 21, 19, 15, 6, 12, 8, 15, 13;
[10]     55, 31, 19, 15, 16, 12, 8, 15, 13, 18.

Maple

t := (n, k) -> NumberTheory:-Divisors(k) union {seq(k*j, j=2..n/k)}:
T := (n, k) -> add(j, j = t(n, k)):
for n from 1 to 10 do seq(T(n, k), k=1..n) od;

Crossrefs

T(n, 1) = A000217(n), T(n, n) = A000203(n), T(2n, n) = A224880(n).

Cf. A339491, A339492, A339489.

Sequence in context: A034188 A184849 A335870 * A336422 A040007 A351024

Adjacent sequences: A339493 A339494 A339495 * A339497 A339498 A339499

Keyword

nonn,tabl

Author

Peter Luschny, Dec 31 2020

Status

approved