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A356164 a(n) is the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

%I A356164 #14 Jul 28 2022 21:16:00
%S A356164 1,2,2,4,3,2,5,8,4,6,7,4,11,10,3,16,13,4,17,12,10,14,19,8,9,22,8,20,
%T A356164 23,6,29,32,14,26,5,4,31,34,22,24,37,10,41,28,6,38,43,16,25,18,26,44,
%U A356164 47,8,21,40,34,46,53,12,59,58,20,64,33,14,61,52,38,10,67,8,71,62,9,68,7,22,73,48,16,74,79,20,39,82
%N A356164 a(n) is the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
%C A356164 a(n) is the smallest positive k such that A191002(k) is a multiple of n.
%H A356164 Antti Karttunen, <a href="/A356164/b356164.txt">Table of n, a(n) for n = 1..16384</a>
%H A356164 Antti Karttunen, <a href="/A356164/a356164.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A356164 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A356164 a(n) = n - A356165(n).
%F A356164 For n >= 2, a(A000040(n)) = A000040(n-1).
%o A356164 (PARI)
%o A356164 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A356164 A356164(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(k)));
%Y A356164 Cf. A000040, A003961, A191002, A356165, A356166, A356167, A356168, A356169.
%Y A356164 Cf. also A344005, A355944.
%K A356164 nonn
%O A356164 1,2
%A A356164 _Antti Karttunen_, Jul 28 2022