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A079551
a(n) = Sum_{primes p <= n} d(p-1), where d() = A000005.
3
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
OFFSET
0,4
REFERENCES
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.
LINKS
Enrico Bombieri, John B. Friedlander, and Henryk Iwaniec, Primes in arithmetic progressions to large moduli, Acta Mathematica, Vol. 156, No. 1 (1986), pp. 203-251.
Heini Halberstam, Footnote to the Titchmarsh-Linnik divisor problem, Proceedings of the American Mathematical Society, Vol. 18, No. 1 (1967), pp. 187-188.
Yurii Vladimirovich Linnik, New versions and new uses of the dispersion methods in binary additive problems, Doklady Akademii Nauk SSSR, Vol. 137, No. 6. (1961), pp. 1299-1302 (in Russian).
Gaetano Rodriquez, Sul problema dei divisori di Titchmarsh, Bollettino dell'Unione Matematica Italiana, Vol. 20, No. 3 (1965), pp. 358-366.
E. C. Titchmarsh, A divisor problem, Rendiconti del Circolo Matematico di Palermo (1884-1940), December 1930, Volume 54, Issue 1, pp. 414-429.
FORMULA
Several asymptotic estimates are known: see Sándor et al.
a(n) ~ (zeta(2)*zeta(3)/zeta(6)) * n. - Amiram Eldar, Jul 22 2019
MATHEMATICA
a[n_] := Sum[DivisorSigma[0, p-1], {p, Select[Range[n], PrimeQ]}]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 26 2015 *)
PROG
(PARI) a(n) = sum(p=1, n, if (isprime(p), numdiv(p-1))); \\ Michel Marcus, Aug 03 2018
CROSSREFS
Row sums of triangle A143540. - Gary W. Adamson, Aug 23 2008
Sequence in context: A049318 A325861 A376449 * A182843 A358558 A008805
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 24 2003
STATUS
approved