A097106 a(n) = (Smallest prime power >= n) - (greatest prime power <= n).

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3, 3, 0, 0, 2, 0, 4, 4, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 5, 5, 5, 5, 0, 4, 4, 4, 0, 2, 0, 4, 4, 4, 0, 2, 0, 4, 4, 4, 0, 6, 6, 6, 6, 6, 0, 2, 0, 3, 3, 0, 3, 3, 0, 4, 4, 4, 0, 2, 0, 6, 6, 6, 6, 6, 0, 2, 0, 2, 0, 6, 6, 6, 6, 6, 0, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 2, 0, 4, 4

Offset: 1

Author

Reinhard Zumkeller, Sep 15 2004

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000015, A031218, A000961, A072680.

Programs

Mathematica

sp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m++]; m]];
gp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m--]; m]];
a[n_] := sp[n] - gp[n];
Array[a, 100] (* Jean-François Alcover, Dec 02 2021 *)

PARI

A000015(n) = if(1==n, n, while(!isprimepower(n), n++); n);
A031218(n) = if(1==n, n, while(!isprimepower(n), n--); n);
A097106(n) = (A000015(n) - A031218(n)); \\ Antti Karttunen, Sep 23 2018

Formula

a(n) = A000015(n) - A031218(n);

a(n) = 0 iff n is a power of a prime (in A000961).