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%I #22 Feb 06 2022 06:50:34
%S 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,
%T 35,35,35,35,41,41,49,49,49,49,49,49,58,58,58,58,66,66,74,74,74,74,78,
%U 78,78,78,78,78,84,84,84,84,84,84,88,88,100,100,100,100,100,100,108,108,108,108
%N a(n) = Sum_{primes p <= n} d(p-1), where d() = A000005.
%D Yuri V. Linnik, The dispersion method in binary additive problems, American Mathematical Society, 1963, chapter VIII.
%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer, 2006, section II.11, p. 49.
%H Amiram Eldar, <a href="/A079551/b079551.txt">Table of n, a(n) for n = 0..10000</a>
%H Enrico Bombieri, John B. Friedlander, and Henryk Iwaniec, <a href="https://projecteuclid.org/euclid.acta/1485890416">Primes in arithmetic progressions to large moduli</a>, Acta Mathematica, Vol. 156, No. 1 (1986), pp. 203-251.
%H Heini Halberstam, <a href="https://doi.org/10.1090/S0002-9939-1967-0204379-6">Footnote to the Titchmarsh-Linnik divisor problem</a>, Proceedings of the American Mathematical Society, Vol. 18, No. 1 (1967), pp. 187-188.
%H Yurii Vladimirovich Linnik, <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dan&paperid=24909&option_lang=eng">New versions and new uses of the dispersion methods in binary additive problems</a>, Doklady Akademii Nauk SSSR, Vol. 137, No. 6. (1961), pp. 1299-1302 (in Russian).
%H Gaetano Rodriquez, <a href="https://eudml.org/doc/195925">Sul problema dei divisori di Titchmarsh</a>, Bollettino dell'Unione Matematica Italiana, Vol. 20, No. 3 (1965), pp. 358-366.
%H E. C. Titchmarsh, <a href="https://doi.org/10.1007/BF03021203">A divisor problem</a>, Rendiconti del Circolo Matematico di Palermo (1884-1940), December 1930, Volume 54, Issue 1, pp. 414-429.
%F Several asymptotic estimates are known: see Sándor et al.
%F a(n) ~ (zeta(2)*zeta(3)/zeta(6)) * n. - _Amiram Eldar_, Jul 22 2019
%t a[n_] := Sum[DivisorSigma[0, p-1], {p, Select[Range[n], PrimeQ]}]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 26 2015 *)
%o (PARI) a(n) = sum(p=1, n, if (isprime(p), numdiv(p-1))); \\ _Michel Marcus_, Aug 03 2018
%Y Cf. A000005, A079552, A082695.
%Y Row sums of triangle A143540. - _Gary W. Adamson_, Aug 23 2008
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 24 2003
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