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A064609 Partial sums of A034448: sum of unitary divisors from 1 to n. 8
1, 4, 8, 13, 19, 31, 39, 48, 58, 76, 88, 108, 122, 146, 170, 187, 205, 235, 255, 285, 317, 353, 377, 413, 439, 481, 509, 549, 579, 651, 683, 716, 764, 818, 866, 916, 954, 1014, 1070, 1124, 1166, 1262, 1306, 1366, 1426, 1498, 1546, 1614, 1664, 1742, 1814, 1884 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = a(n-1) + A034448(n) = Sum_{j=1..n} usigma(j) where usigma(j) = A034448(j).

a(n) ~ Pi^2 * n^2 / (12*Zeta(3)). - Vaclav Kotesovec, Jan 11 2019

MATHEMATICA

Accumulate@ Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &], {n, 52}] (* Michael De Vlieger, Mar 18 2017 *)

PROG

(PARI) usigma(n)= { local(f, s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }

{ a=0; for (n=1, 1000, a+=usigma(n); write("b064609.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 20 2009

(Python)

from sympy.ntheory.factor_ import udivisor_sigma

def a(n): return sum(udivisor_sigma(j, 1) for j in range(1, n + 1))

print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Mar 18 2017

CROSSREFS

Cf. A034448, A064611.

Sequence in context: A312211 A034856 A183865 * A327566 A307159 A312212

Adjacent sequences:  A064606 A064607 A064608 * A064610 A064611 A064612

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 24 2001

STATUS

approved

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Last modified November 28 05:17 EST 2020. Contains 338699 sequences. (Running on oeis4.)