A327938 - OEIS

%I #13 Nov 07 2022 07:40:18

%S 1,2,3,1,5,6,7,2,9,10,11,3,13,14,15,1,17,18,19,5,21,22,23,6,25,26,1,7,

%T 29,30,31,2,33,34,35,9,37,38,39,10,41,42,43,11,45,46,47,3,49,50,51,13,

%U 53,2,55,14,57,58,59,15,61,62,63,1,65,66,67,17,69,70,71,18,73,74,75,19,77,78,79,5,3,82,83,21,85,86,87,22

%N Multiplicative with a(p^e) = p^(e mod p).

%C All terms are in A048103.

%H Antti Karttunen, <a href="/A327938/b327938.txt">Table of n, a(n) for n = 1..20000</a>

%F Multiplicative with a(p^e) = p^(e mod p).

%F a(n) = n / A327939(n).

%F For all n, A129251(a(n)) = 0, A327936(a(n)) = 1.

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1/(1+1/p^p)) = 0.38559042841678887219... . - _Amiram Eldar_, Nov 07 2022

%t f[p_, e_] := p^Mod[e, p]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 07 2022 *)

%o (PARI) A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]%f[k,1])); factorback(f); };

%Y Cf. A048103, A129251, A327936, A327937, A327939, A327965.

%Y Differs from A065883 for the first time at n=27.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Oct 01 2019