A307137 - OEIS

%I #25 Mar 29 2019 10:47:52

%S 68,17500,5053176,435034872,3079148398,107924794257,122918945808

%N Terms of A194269 that are not squares of primes.

%C A194269 lists the integers j that satisfy Sum_{i=1..k} d(i)^i = j+1 for some k where d() is the sorted list of divisors of j.

%C All squares of primes (A001248) are in A194269 (with k=2), but some terms of A194269 are not in A001248.

%C So the sequence can be thought of as the set of integers that satisfy Sum_{i=1..k} d(i)^i = j+1 for k > 2.

%C Also in the sequence are 63602175290616, 27232626132792608, 131685306017557752 and 1125089196456707568267636780. - _Daniel Suteu_, Mar 28 2019

%C a(8) > 2.5*10^11. 146891545244361186001164385301664828062299990188246080274986418 and 1074195891803336036687617104130500495489848428998310547357799403665 are also terms. - _Giovanni Resta_, Mar 29 2019

%e The divisors of 68 are 1, 2, 4, 17, 34, 68; 1^1 + 2^2 + 4^3 = 69, so 68 is a term.

%o (PARI) isok1(n) = {my(d=divisors(n), s=0); for(k=1, #d, s += d[k]^k; if (s == n+1, return (k)); if (s > n+1, break););} \\ A194269

%o isok2(n) = issquare(n) && isprime(sqrtint(n));

%o isok(n) = isok1(n) && !isok2(n);

%Y Cf. A001248, A194269.

%K nonn,more

%O 1,1

%A _Michel Marcus_, Mar 26 2019

%E a(6)-a(7) from _Giovanni Resta_, Mar 29 2019