A327573 Partial sums of the number of infinitary divisors function: a(n) = Sum_{k=1..n} id(k), where id is A037445.

1, 3, 5, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 41, 43, 45, 49, 51, 55, 59, 63, 65, 73, 75, 79, 83, 87, 89, 97, 99, 103, 107, 111, 115, 119, 121, 125, 129, 137, 139, 147, 149, 153, 157, 161, 163, 167, 169, 173, 177, 181, 183, 191, 195, 203, 207, 211, 213, 221

Offset

1,2

Comments

Differs from A306069 at n >= 16.

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Graeme L. Cohen and Peter Hagis, Jr., Arithmetic functions associated with infinitary divisors of an integer, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383.

Formula

a(n) ~ 2 * c * n * log(n), where c = 0.366625... (A327576). [Corrected by Amiram Eldar, May 07 2021]

Mathematica

f[p_, e_] := 2^DigitCount[e, 2, 1]; id[1] = 1; id[n_] := Times @@ (f @@@ FactorInteger[n]); Accumulate[Array[id, 100]]

Crossrefs

Cf. A037445, A327576.

Cf. A006218 (all divisors), A064608 (unitary), A306069 (bi-unitary), A145353 (exponential).

Sequence in context: A156982 A224195 A338129 * A306069 A270807 A157048

Adjacent sequences: A327570 A327571 A327572 * A327574 A327575 A327576

Keyword

nonn

Author

Amiram Eldar, Sep 17 2019

Status

approved