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I've been wondering who/what could use the hash160 field of the blockchain.info API.

For example, for the address "1N3Xxt13zbDLU66aSBiMB7AjRW1UiUFAau", the hash160 value is e6d55202fe5e9e9e2973aab12bbb91db67948138, which is roughly the hex format of the address (00e6d55202fe5e9e9e2973aab12bbb91db6794813840292932).

As it seems truncated, it seems that we miss some bits of information.

Also, I've seen that the hash160 should be calculated differently, so why this value is present?

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The information that the company displaying is correct, though there's no standard for displaying this to end users. You have unpacked the address and included the version byte and checksum as well in the string, note that only the hash160 is used in a pay to pubkey bitcoin script.

Base58Check    1N3Xxt13zbDLU66aSBiMB7AjRW1UiUFAau
Decoded        0x00e6d55202fe5e9e9e2973aab12bbb91db6794813840292932

Version Byte   0x00 
Hash160        0xe6d55202fe5e9e9e2973aab12bbb91db67948138
Checksum       0x40292932

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