Numbers by Position

Google Sheets, 35 bytes

=ArrayFormula(Rept(Row(1:9),Row(1:9

Sheets will automatically add three trailing parentheses when you exit the cell. Output is one line per row.

Bash + Core utilities, 27, 25 bytes

seq -f8d%f*7-v1+2/n 45|dc

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Changed seq formatting from %0.f to %f for a 2-byte savings.

Modified to print on one line, with no delimiters, instead of having a newline after each number, just because I like that better. Same number of bytes.

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This uses the formula $$\left\lfloor\frac{\big\lfloor\sqrt{8n-7}\big\rfloor+1}2\right\rfloor$$

for the \$n^{th}\$ digit, where \$n\$ goes from 1 to 45.

05AB1E, 3 bytes

9L×

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9L    Build a list from 1 to 9 {1, 2, 3, 4, 5, 6, 7, 8, 9}
×     copy each number that many times