Make formula disregard other formula entry if blank

[DHFE]

I have a group of possible data entries, these contain whole numbers.
I have a separate sheet which collates all these entries into one table using formulas like - if('sheet1'!A1<1,"",'sheet1'!A1) so as to return a blank if there is no entry, as the minimum will be 1.

However I have other formulas which I want to create one table from only the entries which are not blank, and remove any which are (so I don't get spaces in the final table).
Currently because the second formula knows that the first one exists and the cell is not in fact blank it returns a blank cell rather than ignoring it and moving to the next which isn't blank.

If I manually enter the data into the first table the second table completes as I want it to (without the empty cells), but with the formula it includes the empty cells.

In the Example - I've collected the data from Sheets 1 + 2 into the 1st table (A-F) on Sheet 3, and I want it all displayed in the 2nd table (H,I) on sheet 3 without any blanks.
Example.xlsx
You will see if you delete the formula in the blank cells (A-F) on sheet 3 that the 2nd table shrinks.

[Kaper]

within subtotal use function 2 not 3.

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of course again array formula (ctrl+shift+enter committed)

to make output nicer (get rid of errors) you can nest it within IFERROR:

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and you can adjust I2:

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[DHFE]

that's great thanks

[FDibbins]

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Thanks.

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[DHFE]

sorry, got a bit caught up at work forgot to mark as solved. I give everyone who helps me solve my problems rep...