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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 (list; graph; refs; listen; history; text; internal format)
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

Amiram Eldar, Table of n, a(n) for n = 0..10000

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

Cf. A000005, A079552, A082695.

Row sums of triangle A143540. [Gary W. Adamson, Aug 23 2008]

Sequence in context: A290966 A049318 A325861 * A182843 A008805 A188270

Adjacent sequences:  A079548 A079549 A079550 * A079552 A079553 A079554

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 24 2003

STATUS

approved

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Last modified October 23 09:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)