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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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^3 * log(n), where c = 0.366625... (A327576).

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: A003532 A156982 A224195 * A306069 A270807 A157048

Adjacent sequences:  A327570 A327571 A327572 * A327574 A327575 A327576

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 17 2019

STATUS

approved

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Last modified February 24 22:57 EST 2020. Contains 332216 sequences. (Running on oeis4.)