cp's OEIS Frontend

A378982 a(n) = (A003961(n)-(1+sigma(n))) mod (A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

%I A378982 #7 Dec 13 2024 09:39:51
%S A378982 0,0,0,0,0,2,2,0,4,0,0,16,2,3,0,0,0,35,2,20,9,2,4,74,0,0,13,42,0,32,4,
%T A378982 0,0,2,0,133,2,1,0,98,0,68,2,3,11,4,4,280,17,6,1,5,4,254,18,176,0,2,0,
%U A378982 146,4,1,21,0,1,50,2,9,6,86,0,479,4,8,25,11,2,86,2,380,40,2,4,270,24,8,15,170,6,290,4,15
%N A378982 a(n) = (A003961(n)-(1+sigma(n))) mod (A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%H A378982 Antti Karttunen, <a href="/A378982/b378982.txt">Table of n, a(n) for n = 1..32768</a>
%H A378982 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A378982 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378982 a(n) = (A286385(n)-1) mod A252748(n).
%o A378982 (PARI)
%o A378982 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378982 A378982(n) = ((A003961(n)-(sigma(n)+1))%((2*n)-A003961(n)));
%Y A378982 Cf. A000203, A003961, A252748, A286385, A378983 (positions of 0's).
%Y A378982 Cf. also A378981.
%K A378982 nonn
%O A378982 1,6
%A A378982 _Antti Karttunen_, Dec 13 2024