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A061503
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a(n) = Sum_{k=1..n} tau(k^2), where tau is the number of divisors function A000005.
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7
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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
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of pairs of positive integers <= n with their LCM <= n. - Andrew Howroyd, Sep 01 2019
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REFERENCES
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Mentioned by Steven Finch in a posting to the Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Jun 13 2001.
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LINKS
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FORMULA
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a(n) = Sum_{j=1..n^2} floor(n/A019554(j)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002
a(n) ~ 3*n/Pi^2 * (log(n)^2 + log(n)*(-2 + 6*g - 24*z/Pi^2) + 2 - 6*g + 6*g^2 - 6*sg1 + 288*z^2/Pi^4 - 24*(-z + 3*g*z + z2)/ Pi^2), where g is the Euler-Mascheroni constant A001620, sg1 is the first Stieltjes constant (see A082633), z = Zeta'(2) (see A073002), z2 = Zeta''(2) = A201994. - Vaclav Kotesovec, Jan 30 2019
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MAPLE
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with(numtheory): a:=n->add(tau(k^2), k=1..n): seq(a(n), n=1..60); # Muniru A Asiru, Mar 09 2019
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MATHEMATICA
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PROG
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(PARI) for (n=1, 1024, write("b061503.txt", n, " ", sum(k=1, n, numdiv(k^2)))) \\ Harry J. Smith, Jul 23 2009
return add(tau(k^2) for k in (1..n))
(GAP) List([1..60], n->Sum([1..n], k->Tau(k^2))); # Muniru A Asiru, Mar 09 2019
(Python)
from math import prod
from sympy import factorint
def A061503(n): return sum(prod(2*e+1 for e in factorint(k).values()) for k in range(1, n+1)) # Chai Wah Wu, May 10 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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