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A061503 Sum_{k<=n} (tau(k^2)), where tau is the number of divisors function A000005. 5
1, 4, 7, 12, 15, 24, 27, 34, 39, 48, 51, 66, 69, 78, 87, 96, 99, 114, 117, 132, 141, 150, 153, 174, 179, 188, 195, 210, 213, 240, 243, 254, 263, 272, 281, 306, 309, 318, 327, 348, 351, 378, 381, 396, 411, 420, 423, 450, 455, 470, 479, 494, 497 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Mentioned by Steven Finch in a posting to the Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Jun 13 2001.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1024

Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, vol. 101, (2002), pp. 105-114.

FORMULA

a(n) = Sum_{1<=j<=n^2} (floor(n/A019554(j))), - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002

a(n) = Sum(i=1..n, 2^omega(i) * floor(n/i)) . - Enrique Pérez Herrero, Sep 15 2012

a(n) ~ 3/Pi^2 * n log^2 n. - Charles R Greathouse IV, Nov 08 2012

MATHEMATICA

DivisorSigma[0, Range[60]^2] // Accumulate (* Jean-François Alcover, Nov 25 2013 *)

PROG

(PARI) for (n=1, 1024, write("b061503.txt", n, " ", sum(k=1, n, numdiv(k^2)))) \\ Harry J. Smith, Jul 23 2009

(PARI) t=0; v=vector(60, n, t+=numdiv(n^2)) \\ Charles R Greathouse IV, Nov 08 2012

(Sage) def A061503(n) :

    tau = sloane.A000005

    return add(tau(k^2) for k in (1..n))

[ A061503(i) for i in (1..19)] # Peter Luschny, Sep 15 2012

CROSSREFS

Cf. A000005, A061502. Partial sums of A048691.

Sequence in context: A047535 A182989 A190442 * A134659 A075624 A008333

Adjacent sequences:  A061500 A061501 A061502 * A061504 A061505 A061506

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 14 2001

EXTENSIONS

Name corrected by Peter Luschny, Sep 15 2012

STATUS

approved

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Last modified December 7 07:15 EST 2016. Contains 278841 sequences.