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%I #22 Sep 14 2019 06:38:59
%S 2,12,58,238,3120,6856,29788,50650,65520,161046,262126,300760,1295026,
%T 3442948,9393928,13997518,21253930,49430860,84604516,95443990,
%U 237176656,329939368,384240580,487443400,633839776,893871732,904231060,1284365500,1605723208,3183010108,3301293166,3588604288,3936827536
%N Numbers n of the form p^k - k = q^i - i for primes p < q.
%H Charles R Greathouse IV, <a href="/A268594/b268594.txt">Table of n, a(n) for n = 1..10000</a>
%H S. P. Hurd and J. S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Hurd/hurd1.html">Integers that are Sums of Uniform Powers of all their Prime Factors: the sequence A068916</a>, J. of Int. Seq., vol 22 (2019), article 19.3.4.
%e 50650 = 37^3-3 = 50651^1-1.
%o (PARI) is(n)=my(p);sum(e=1,logint(n,2)+1,ispower(n+e,e,&p)&&isprime(p))>1 \\ _Charles R Greathouse IV_, Feb 08 2016
%o (PARI) list(lim)=my(v=List([2]),q,n); for(e=3,logint(1+lim\=1,2), forprime(p=2, sqrtnint(lim+e,e), if(sum(i=1,e-1, n=p^e-e; ispower(n+i,i,&q) && isprime(q)), listput(v,n)))); Set(v) \\ _Charles R Greathouse IV_, Feb 08 2016
%Y See A268595 for values of p and A268596 for values of q.
%Y Cf. A178251.
%K nonn
%O 1,1
%A _Jud McCranie_, Feb 07 2016
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