cp's OEIS Frontend

A336851 a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.

%I A336851 #25 Jul 03 2023 14:50:19
%S A336851 0,1,1,4,1,9,1,13,6,11,1,33,1,15,13,40,1,49,1,41,17,17,1,105,8,21,31,
%T A336851 57,1,87,1,121,19,23,19,178,1,27,23,131,1,123,1,65,73,33,1,321,12,81,
%U A336851 25,81,1,249,21,183,29,35,1,309,1,41,97,364,25,141,1,89,35,153,1,565,1,45,97,105,25,177,1,401,156,47
%N A336851 a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.
%C A336851 Even terms occur on square n, odd terms on nonsquare n.
%C A336851 Numbers k such that a(k) = 2^e for e >= 1, are: 4, 25, 841, 12769, 66896041, etc., i.e., terms of A073715 squared.
%H A336851 Antti Karttunen, <a href="/A336851/b336851.txt">Table of n, a(n) for n = 1..16384</a>
%H A336851 Antti Karttunen, <a href="/A336851/a336851.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336851 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A336851 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336851 a(n) = A003973(n) - A003961(n) = A000203(A003961(n)) - A003961(n).
%F A336851 a(n) = A001065(A003961(n)).
%F A336851 a(n) = A336852(n) - A286385(n).
%o A336851 (PARI)
%o A336851 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A336851 A336851(n) = (sigma(A003961(n)) - A003961(n));
%Y A336851 Cf. A000203, A001065, A003961, A003973, A073715, A252748, A286385, A326042, A336852.
%Y A336851 Cf. A336850 [= gcd(a(n),A003961(n))].
%K A336851 nonn
%O A336851 1,4
%A A336851 _Antti Karttunen_, Aug 05 2020
%E A336851 Comments edited by _Antti Karttunen_, Jul 03 2023