A348750 - OEIS

%I #8 Nov 03 2021 18:30:22

%S 1,1,1,23,1,1,3,7,13,1,1,23,2,3,1,305,1,13,2,23,3,1,1,7,39,2,4,69,13,

%T 1,3,69,1,1,3,299,5,2,2,7,1,3,1,23,13,1,2,305,53,39,1,46,23,4,1,21,2,

%U 13,11,23,1,3,39,19501,2,1,29,23,1,3,2,91,3,5,39,46,3,2,2,305,2791,1,9,69,1,1,13,7,11,13,6

%N a(n) = A064989(A064989(sigma(A003961(A003961(n))))), where A003961 shifts the prime factorization of n one step towards larger primes, and A064989 shifts it back towards smaller primes.

%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) = A064989(A326042(A003961(n))).

%F Multiplicative with a(p^e) = A064989(A064989((q^(e+1)-1)/(q-1))), where q = nextPrime(nextPrime(p)).

%o (PARI)

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

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A348750(n) = A064989(A064989(sigma(A003961(A003961(n)))));

%Y Cf. A000203, A003961, A003973, A064989, A326042, A348751 (a(n) < n), A348752 (a(n) > n).

%K nonn,mult

%O 1,4

%A _Antti Karttunen_, Nov 02 2021