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A079551
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a(n) = Sum_{primes p <= n} d(p-1), where d() = A000005.
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3
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0, 0, 1, 3, 3, 6, 6, 10, 10, 10, 10, 14, 14, 20, 20, 20, 20, 25, 25, 31, 31, 31, 31, 35, 35, 35, 35, 35, 35, 41, 41, 49, 49, 49, 49, 49, 49, 58, 58, 58, 58, 66, 66, 74, 74, 74, 74, 78, 78, 78, 78, 78, 78, 84, 84, 84, 84, 84, 84, 88, 88, 100, 100, 100, 100, 100, 100, 108, 108, 108, 108
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OFFSET
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0,4
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REFERENCES
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Yuri V. Linnik, The dispersion method in binary additive problems, American Mathematical Society, 1963, chapter VIII.
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer, 2006, section II.11, p. 49.
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LINKS
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E. C. Titchmarsh, A divisor problem, Rendiconti del Circolo Matematico di Palermo (1884-1940), December 1930, Volume 54, Issue 1, pp. 414-429.
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FORMULA
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Several asymptotic estimates are known: see Sándor et al.
a(n) ~ (zeta(2)*zeta(3)/zeta(6)) * n. - Amiram Eldar, Jul 22 2019
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MATHEMATICA
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a[n_] := Sum[DivisorSigma[0, p-1], {p, Select[Range[n], PrimeQ]}]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 26 2015 *)
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PROG
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(PARI) a(n) = sum(p=1, n, if (isprime(p), numdiv(p-1))); \\ Michel Marcus, Aug 03 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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