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A006146 Sums of prime divisors of Ruth-Aaron numbers (A006145).

%I A006146 #35 Feb 16 2025 08:32:29
%S A006146 5,5,7,18,15,20,44,46,29,31,50,30,20,34,75,162,146,46,14,113,53,66,
%T A006146 333,36,514,318,43,193,279,418,30,121,55,485,200,136,77,37,211,587,
%U A006146 147,269,477,108,136,235,185,290,333,309,493,177,199,223,641,531,182,368
%N A006146 Sums of prime divisors of Ruth-Aaron numbers (A006145).
%D A006146 John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120-122.
%D A006146 Dana Mackenzie, Homage to an itinerant master, Science, vol. 275, p. 759, 1997.
%D A006146 Carol Nelson, David E. Penney, and Carl Pomerance, 714 and 715. Journal of Recreational Mathematics 7(2):87-89, 1974.
%H A006146 Amiram Eldar, <a href="/A006146/b006146.txt">Table of n, a(n) for n = 1..10000</a>
%H A006146 G. Kreweras and Y. Poupard, <a href="/A000806/a000806.pdf">Sur les partitions en paires d'un ensemble fini totalement ordonné</a>, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74. (Annotated scanned copy)
%H A006146 Ivars Peterson, <a href="https://www.sciencenews.org/article/playing-ruth-aaron-pairs">Playing with Ruth-Aaron pairs</a>
%H A006146 Ivars Peterson's MathTrek, <a href="https://web.archive.org/web/20130702062101/http://www.maa.org/mathland/mathland_6_30.html">Playing with Ruth-Aaron Pairs</a> [In the internet archive]
%H A006146 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ruth-AaronPair.html">Ruth-Aaron Pair</a>
%F A006146 a(n) = A008472(A006145(n)) = A008472(A006145(n) + 1). - _Amiram Eldar_, Nov 24 2019
%p A006146 with(numtheory): for n from 1 to 10000 do t0 := 0; t1 := factorset(n);
%p A006146 for j from 1 to nops(t1) do t0 := t0+t1[ j ]; od: s[ n ] := t0; od:
%p A006146 for n from 1 to 9999 do if s[ n ] = s[ n+1 ] then lprint(n,s[ n ]); fi; od:
%t A006146 Cases[Partition[(Plus@@(First@#&/@FactorInteger@#)&/@Range@100000),2,1],{a_,a_}:>a] (* _Hans Rudolf Widmer_, May 31 2024 *)
%o A006146 (Python)
%o A006146 from sympy import primefactors
%o A006146 def aupton(terms):
%o A006146   alst, k, sopfk, sopfkp1 = [], 0, 0, 1
%o A006146   while len(alst) < terms:
%o A006146     k, sopfk, sopfkp1 = k+1, sopfkp1, sum(p for p in primefactors(k+1))
%o A006146     if sopfkp1 == sopfk: alst.append(sopfk)
%o A006146   return alst
%o A006146 print(aupton(58)) # _Michael S. Branicky_, May 05 2021
%Y A006146 Cf. A006145, A008472, A039752, A039753, A039703, A054378.
%K A006146 nonn
%O A006146 1,1
%A A006146 _N. J. A. Sloane_