cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A097106 #11 Dec 02 2021 13:02:38
%S A097106 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,
%T A097106 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,
%U A097106 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
%N A097106 a(n) = (Smallest prime power >= n) - (greatest prime power <= n).
%H A097106 Antti Karttunen, <a href="/A097106/b097106.txt">Table of n, a(n) for n = 1..65537</a>
%F A097106 a(n) = A000015(n) - A031218(n);
%F A097106 a(n) = 0 iff n is a power of a prime (in A000961).
%t A097106 sp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m++]; m]];
%t A097106 gp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m--]; m]];
%t A097106 a[n_] := sp[n] - gp[n];
%t A097106 Array[a, 100] (* _Jean-François Alcover_, Dec 02 2021 *)
%o A097106 (PARI)
%o A097106 A000015(n) = if(1==n, n, while(!isprimepower(n), n++); n);
%o A097106 A031218(n) = if(1==n, n, while(!isprimepower(n), n--); n);
%o A097106 A097106(n) = (A000015(n) - A031218(n)); \\ _Antti Karttunen_, Sep 23 2018
%Y A097106 Cf. A000015, A031218, A000961, A072680.
%K A097106 nonn,look
%O A097106 1,6
%A A097106 _Reinhard Zumkeller_, Sep 15 2004