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A327573
Partial sums of the number of infinitary divisors function: a(n) = Sum_{k=1..n} id(k), where id is A037445.
4
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
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. A006218 (all divisors), A064608 (unitary), A306069 (bi-unitary), A145353 (exponential).
Sequence in context: A156982 A224195 A338129 * A306069 A270807 A157048
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 17 2019
STATUS
approved