

A339496


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


3



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
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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 A110634
Adjacent sequences: A339493 A339494 A339495 * A339497 A339498 A339499


KEYWORD

nonn,tabl


AUTHOR

Peter Luschny, Dec 31 2020


STATUS

approved



