Search: id:A006145
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%I A006145
%S A006145 5,24,49,77,104,153,369,492,714,1682,2107,2299,2600,2783,5405,6556,
%T A006145 6811,8855,9800,12726,13775,18655,21183,24024,24432,24880,25839,
%U A006145 26642,35456,40081,43680,48203,48762,52554,61760,63665,64232,75140
%N A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors 
               of n+1.
%C A006145 So called because 714 is Babe Ruth's lifetime home run record, Hank Aaron's 
               715th home run broke this record and 714 and 715 have the same sum 
               of prime divisors - David W. Wilson
%D A006145 John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120-122.
%D A006145 C. Nelson, D. E. Penney and C. Pomerance, "714 and 715", J. Recreational 
               Math. 7 (No. 2) 1994, 87-89.
%D A006145 Science, vol. 275, p. 759, 1997.
%D A006145 P. Hoffman, The Man Who Loved Only Numbers, pp. 179-181, Hyperion, NY 
               1998.
%D A006145 J. Roberts, Lure of Integers, pp. 250, MAA 1992.
%D A006145 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, 
               pp. 159-160, Penguin 1986.
%H A006145 Joe K. Crump, <a href="http://www.immortaltheory.com/NumberTheory/default.asp?SubPage=RuthAaron.htm">
               Ruth-Aaron Pairs-an algorithm</a>
%H A006145 Ivars Petersen, <a href="http://www.maa.org/mathland/mathland_6_30.html">
               Related page</a>
%H A006145 T. Trotter,Jr., <a href="http://www.trottermath.net/numthry/rutharon.html">
               Ruth-Aaron Numbers</a>
%H A006145 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Ruth-AaronPair.html">Ruth-Aaron Pair</a>
%p A006145 with(numtheory): for n from 1 to 10000 do t0 := 0; t1 := factorset(n);
%p A006145 for j from 1 to nops(t1) do t0 := t0+t1[ j ]; od: s[ n ] := t0; od:
%p A006145 for n from 1 to 9999 do if s[ n ] = s[ n+1 ] then lprint(n,s[ n ]); fi; 
               od:
%Y A006145 Cf. A006146, A039752, A039753, A054378.
%Y A006145 Sequence in context: A056234 A030766 A063143 this_sequence A085646 A121546 
               A135703
%Y A006145 Adjacent sequences: A006142 A006143 A006144 this_sequence A006146 A006147 
               A006148
%K A006145 nonn
%O A006145 1,1
%A A006145 N. J. A. Sloane (njas(AT)research.att.com).

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