A336853 - OEIS

%I #11 Aug 10 2020 00:19:32

%S 0,1,2,5,2,9,4,19,16,11,2,33,4,19,20,65,2,57,4,43,34,17,6,111,24,25,

%T 98,71,2,75,6,211,32,23,42,189,4,31,46,149,2,123,4,73,130,41,6,357,72,

%U 97,44,101,6,321,36,241,58,35,2,255,6,49,212,665,54,129,4,103,76,161,2,603,6,49,170,131,66,177,4,487,544

%N a(n) = A003961(n) - n, where A003961 is the prime shift towards larger primes.

%H Antti Karttunen, <a href="/A336853/b336853.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A336853/a336853.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A003961(n) - n.

%F a(n) = A252748(n) + n.

%F A000035(a(n)) = 1 - A000035(n).

%o (PARI) A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); };

%Y Cf. A000035, A001359 (positions of 2's), A003961, A252748, A336852 (inverse Möbius transform).

%K nonn

%O 1,3

%A _Antti Karttunen_, Aug 09 2020