JavaScript (Node.js), 82 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

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Input as array of characters, output a number.

JavaScript (Node.js), 80 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'056 3421'[c%30%9]*p,q=p=1)&&q

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Input an array of codepoints, output a number.

I believe someone may find out better hash functions.

JavaScript (Node.js), 81 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)``**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

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Input as array of characters, output a number.

Saved 1 byte by Shaggy.

JavaScript (Node.js), 79 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)``**'056 3421'[c%30%9]*p,q=p=1)&&q

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Input an array of codepoints, output a number.

Saved 1 byte by Shaggy.

I believe someone may find out better hash functions.

JavaScript (Node.js), 82 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

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Input as array of characters, output a number.

JavaScript (Node.js), 82 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

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Input as array of characters, output a number.

JavaScript (Node.js) , 80 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'056 3421'[c%30%9]*p,q=p=1)&&q

Try it online!

Input an array of codepoints, output a number.

I believe someone may find out better hash functions.

JavaScript (Node.js), 82 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

Try it online!

JavaScript (Node.js), 82 bytes

s=>s.map(c=>q*=(g=v=>p%v--?g(v):v?g(p++):p*p)(0)**'0s~|A()'.indexOf(c)*p,q=p=1)&&q

Try it online!

Input as array of characters, output a number.