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COMMENTS
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Prime p divides a(p-1). n divides a(n-1) for all prime n and all odd composite n.
p divides a((p+1)/2) for prime p = {3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, ...} = A003629 (Primes congruent to {3,5} mod 8).
p divides a((p+3)/4) for prime p = {13, 73, 97, 109, 181, 229, 241, 277, 337, 409, 421, 457, 541, 709, 733, 757, 829, ...} = A107141 (Primes of the form 4x^2+9y^2).
p divides a((p+5)/6) for prime p = {43, 61, 79, 109, 151, 163, 181, 193, 313, 337, 433, 523, 577, 631, 643, 673, 787, 829, 907, 991, ...}.
p divides a((p+7)/8) for prime p = {113, 137, 569, 641, 673, 1129, 1289, 1297, 1481, 1801, ...}.
p divides a((3p-1)/2) for prime p = {5, 7, 13, 23, 29, 31, 37, 47, 53, 61, 71, 79, 101, 103, 109, 127, 149, 151, 157, 167, 173, 181, 191, 197, 199, ...} = A003628 (Primes congruent to {5, 7} mod 8).
p^2 divides a((3p-1)/2) for prime p = {5, 13, 173, 5501, ...} = A124924.
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