A097106 - OEIS

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

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OFFSET

1,6

LINKS

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

FORMULA

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

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

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];