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(PARI) / * alternate program; does it give the least terms? */

isokplus(n, plus) = {my(vd = divisors(n)); for (k=1, #vd - 1, r = vd[k+1]/vd[k]; if (numerator(r) != denominator(r) + plus, return(0)); ); return(1); }

findqq(p) = {ok = 0; ip = 1; while (!ok, ik = 1; while (!ok, if (isprime(q= ik*p^ip+(p-1)) && isokplus(p^ip*q, p-1), return([p^ip, q])); ik++; if (ik > p, break); ); ip ++; ); return ([]); }

listff(nn) = {for (n=1, nn, p = prime(n); v = findqq(p); pp = v[1]; q = v[2]; print1(pp*q, ", "); ); }

p=23, a(9) <= 78317141783; p=73, a(21) <= 151362235513.

p=29, a(10) <= 176994576151121533000319046029;

p=47, a(15) <= 7654455761751330268890575447204341560894807321851181994954582195247;

p=61, a(18) <= 9876832533549882665273701;

p=67, a(19) <= 4483224940666198270986387212125921182677251147716597066996042973310060661858239362623427;

p=71, a(20) <= 269277687648484922419868038102292093702042951;

p=73, a(21) <= 151362235513.

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6, 15, 725, 91, 15851, 30589, 6977093777, 703

For primes 17 < p < 100, index n, prime p and known values: (8, 19, 703), (11, 31, 1891), (12, 37, 270), (13, 41, 2893001), (14, 43, 6324702343), (16, 53, 8036549), (17, 59, 12319259), (22, 79, 12403), (23, 83, 48023219), (24, 89, 63439289), (25, 97, 18721).

For some other primes, I found possible values, were found, but they may not be the least.

p=17, a(7) <= 6977093777; p=23, a(9) <= 78317141783; p=73, a(21) <= 151362235513.

For primes 17 < p < 100, index n, prime p and known values: (8, 19, 703), (11, 31, 1891), (12, 37, 270), (13, 41, 2893001), (14, 43, 6324702343), (16, 53, 8036549), (17, 59, 12319259), (22, 79, 12403), (23, 83, 48023219), (24, 89, 63439289), (25, 97, 18721).

p=17, a(7) <= 6977093777; p=23, a(9) <= 78317141783; p=73, a(21) <= 151362235513.

p=43, a(14) <= 6324702343; p=73, a(21) <= 151362235513.

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