A080732 Smallest distance from n to a prime power (as defined in A246655).

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2

Offset: 1

Author

Benoit Cloitre, Mar 08 2003

Keywords

• nonn

Comments

a(n)=min (abs(n-k) : where k runs through the prime powers)

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051699, A246547, A301295.

There are four different sequences which may legitimately be called "prime powers": A000961 (p^k, k >= 0), A246655 (p^k, k >= 1), A246547 (p^k, k >= 2), A025475 (p^k, k=0 and k >= 2). When you refer to "prime powers", be sure to specify which of these you mean. - N. J. A. Sloane, Mar 24 2018

Programs

Mathematica

nn = 100; pp = Select[Range[2, Prime[1 + PrimePi[nn]]], Length[FactorInteger[#]] == 1 &]; Table[Min[Abs[n - pp]], {n, nn}] (* T. D. Noe, Mar 14 2012 *)