In all these cases, the right hand side is a divisor of the left hand side:
Term (and its factorization) A005941(term)
1 (unity) -> 1
3 (prime) -> 3
5 (prime) -> 5
3125 = 5^5 -> 125 = 5^3
7875 = 3^2 * 5^3 * 7 -> 375 = 3 * 5^3
12005 = 5 * 7^4 -> 245 = 5 * 7^2
13365 = 3^5 * 5 * 11 -> 1215 = 3^5 * 5
22869 = 3^3 * 7 * 11^2 -> 847 = 7 * 11^2
23595 = 3 * 5 * 11^2 * 13 -> 715 = 5 * 11 * 13
46475 = 5^2 * 11 * 13^2 -> 845 = 5 * 13^2
703395 = 3^2 * 5 * 7^2 * 11 * 29 -> 33495 = 3 * 5 * 7 * 11 * 29
985439 = 7^3 * 13^2 * 17 -> 2873 = 13^2 * 17
2084775 = 3 * 5^2 * 7 * 11 * 19^2 -> 12635 = 5 * 7 * 19^2
2675673 = 3^5 * 7 * 11^2 * 13 -> 11583 = 3^4 * 11 * 13
13619125 = 5^3 * 13 * 17^2 * 29 -> 36125 = 5^3 * 17^2
19144125 = 3^2 * 5^3 * 7 * 11 * 13 * 17 -> 21879 = 3^2 * 11 * 13 * 17.
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