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

1,1

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.

Example

50650 = 37^3-3 = 50651^1-1.

Prog

(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
(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

Crossrefs

See A268595 for values of p and A268596 for values of q.

Cf. A178251.

Sequence in context: A177782 A005038 A094780 * A100103 A281028 A054145

Adjacent sequences: A268591 A268592 A268593 * A268595 A268596 A268597

Keyword

nonn

Author

Jud McCranie, Feb 07 2016

Status

approved