A356165 - OEIS

%I #12 Jul 28 2022 21:16:03

%S 0,0,1,0,2,4,2,0,5,4,4,8,2,4,12,0,4,14,2,8,11,8,4,16,16,4,19,8,6,24,2,

%T 0,19,8,30,32,6,4,17,16,4,32,2,16,39,8,4,32,24,32,25,8,6,46,34,16,23,

%U 12,6,48,2,4,43,0,32,52,6,16,31,60,4,64,2,12,66,8,70,56,6,32,65,8,4,64,46,4,41,32,6,84,36

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

%H Antti Karttunen, <a href="/A356165/b356165.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = n - A356164(n).

%F For all odd primes p, a(p) = A001223(A000720(p)-1).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A356165(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(n-k)));

%Y Cf. A000079 (positions of zeros), A000720, A001223, A003961, A191002, A356164, A356166.

%Y Cf. also A355945.

%K nonn

%O 1,5

%A _Antti Karttunen_, Jul 28 2022