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

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)
A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A336840(n) = sumdiv(n, d, A048673(d));
(PARI) A336840(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1/2)*(numdiv(n)+sigma(factorback(f))); };

Crossrefs

Cf. A000005, A003961, A003973, A048673, A113415, A336838, A336839, A336841, A349384, A349385.

Sequence in context: A288091 A057926 A078766 * A253080 A050417 A327613

Adjacent sequences: A336837 A336838 A336839 * A336841 A336842 A336843

Keyword

nonn

Author

Antti Karttunen, Aug 07 2020

Status

approved