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.
%I A085730 #32 Apr 05 2025 09:11:18 %S A085730 1,1,2,2,4,6,4,6,10,12,8,16,18,22,20,18,28,30,16,36,40,42,46,42,52,58, %T A085730 60,32,66,70,72,78,54,82,88,96,100,102,106,108,112,110,100,126,64,130, %U A085730 136,138,148,150,156,162,166,156,172,178,180,190,192,196,198,210 %N A085730 Euler's totient function applied to the sequence of prime powers. %H A085730 Reinhard Zumkeller, <a href="/A085730/b085730.txt">Table of n, a(n) for n = 1..10000</a> %H A085730 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>. %H A085730 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>. %F A085730 a(n) = A000010(A000961(n)). %F A085730 a(p^e) = (p-1)*p^(e-1). %F A085730 a(n) = (A025473(n)-1)*A025473(n)^(A025474(n)-1). %t A085730 f[p_, e_] := (p-1)*p^(e-1); s[n_] := If[n == 1, 1, If[PrimePowerQ[n], f @@ (FactorInteger[n][[1]]), Nothing]]; Array[s, 220] (* _Amiram Eldar_, Apr 05 2025 *) %o A085730 (Haskell) %o A085730 a085730 1 = 1 %o A085730 a085730 n = (p - 1) * p ^ (e - 1) %o A085730 where p = a025473 n; e = a025474 n %o A085730 -- _Reinhard Zumkeller_, Feb 16 2012 %o A085730 (PARI) list(lim)=my(v=List(primes(primepi(lim)))); listput(v,1); for(e=2, log(lim+.5)\log(2),forprime(p=2,(lim+.5)^(1/e),listput(v, p^e))); apply(n->eulerphi(n),vecsort(Vec(v))) \\ _Charles R Greathouse IV_, Apr 30 2012 %Y A085730 Cf. A000010, A000961, A025473, A025474, A207193. %K A085730 nonn %O A085730 1,3 %A A085730 _Reinhard Zumkeller_, Jul 20 2003