A336840 - OEIS

A336840

Inverse Möbius transform of A048673.

1, 3, 4, 8, 5, 14, 7, 22, 17, 18, 8, 42, 10, 26, 26, 63, 11, 65, 13, 55, 38, 30, 16, 124, 30, 38, 80, 81, 17, 100, 20, 185, 44, 42, 50, 206, 22, 50, 56, 164, 23, 148, 25, 94, 127, 62, 28, 368, 68, 117, 62, 120, 31, 316, 58, 244, 74, 66, 32, 318, 35, 78, 189, 550, 74, 172, 37, 133, 92, 196, 38, 626, 41, 86, 174, 159

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OFFSET

1,2

COMMENTS

Arithmetic mean of the number of divisors (A000005) and prime-shifted sigma (A003973), thus a(n) is the average between the number of and the sum of divisors of A003961(n).

The local minima occur on primes p, where p/2 < a(p) <= (p+1).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

FORMULA

a(n) = Sum_{d|n} A048673(d).

a(n) = (1/2) * (A000005(n) + A003973(n)).

a(n) = A113415(A003961(n)). - Antti Karttunen, Jun 01 2022

PROG

(PARI)