A268594 Numbers n of the form p^k - k = q^i - i for primes p < q.
2, 12, 58, 238, 3120, 6856, 29788, 50650, 65520, 161046, 262126, 300760, 1295026, 3442948, 9393928, 13997518, 21253930, 49430860, 84604516, 95443990, 237176656, 329939368, 384240580, 487443400, 633839776, 893871732, 904231060, 1284365500, 1605723208, 3183010108, 3301293166, 3588604288, 3936827536
Offset: 1
Keywords
Examples
50650 = 37^3-3 = 50651^1-1.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- S. P. Hurd and J. S. McCranie, Integers that are Sums of Uniform Powers of all their Prime Factors: the sequence A068916, J. of Int. Seq., vol 22 (2019), article 19.3.4.
Programs
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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
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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