A351456 - OEIS

%I #9 Feb 12 2022 23:47:45

%S 1,1,2,12,1,2,2,4,30,1,6,24,4,2,2,100,4,30,2,12,4,6,8,8,36,4,24,24,1,

%T 2,18,72,12,4,2,360,12,2,8,4,10,4,2,72,30,8,8,200,108,36,8,48,8,24,6,

%U 8,4,1,30,24,16,18,60,1092,4,12,4,48,16,2,36,120,4,12,72,24,12,8,12,100,700,10,16,48,4,2,2,24

%N a(n) = A003958(sigma(A003961(n))), where A003958 is multiplicative with a(p^e) = (p-1)^e, A003961 multiplicative with a(prime(k)^e) = prime(1+k)^e, and sigma is the sum of divisors function.

%H Antti Karttunen, <a href="/A351456/b351456.txt">Table of n, a(n) for n = 1..20000</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 Multiplicative with a(p^e) = A003958(1 + q + ... + q^e), where q = nextPrime(p) = A151800(p).

%F a(n) = A003958(A003973(n)) = A351442(A003961(n)) = A003958(A000203(A003961(n))).

%F a(n) = A351457(n) + A339905(n).

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

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

%o A351456(n) = A003958(sigma(A003961(n)));

%Y Cf. A000203, A003958, A003961, A003973, A151800, A339905, A351442, A351457.

%Y Cf. also A326042.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Feb 12 2022