A327572 Partial sums of an infinitary analog of Euler's phi function: a(n) = Sum_{k=1..n} iphi(k), where iphi is A091732.

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

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 * A370905 A362946 A345983

Adjacent sequences: A327569 A327570 A327571 * A327573 A327574 A327575

Keyword

nonn

Author

Amiram Eldar, Sep 17 2019

Status

approved