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A327572 Partial sums of an infinitary analog of Euler's phi function: a(n) = Sum_{k=1..n} iphi(k), where iphi is A091732. 2
1, 2, 4, 7, 11, 13, 19, 22, 30, 34, 44, 50, 62, 68, 76, 91, 107, 115, 133, 145, 157, 167, 189, 195, 219, 231, 247, 265, 293, 301, 331, 346, 366, 382, 406, 430, 466, 484, 508, 520, 560, 572, 614, 644, 676, 698, 744, 774, 822, 846, 878, 914, 966, 982, 1022, 1040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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) ~ c * n^2, where c = 0.328935... (A327575).

MATHEMATICA

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) - 1); Accumulate[Array[iphi, 52]]

CROSSREFS

Cf. A091732 (iphi), A327575.

Cf. A002088 (sums of phi), A177754 (unitary), A306070 (bi-unitary).

Sequence in context: A191323 A307207 A165288 * A177754 A086795 A064690

Adjacent sequences:  A327569 A327570 A327571 * A327573 A327574 A327575

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 17 2019

STATUS

approved

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)