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 A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1. 19

%I

%S 5,24,49,77,104,153,369,492,714,1682,2107,2299,2600,2783,5405,6556,

%T 6811,8855,9800,12726,13775,18655,21183,24024,24432,24880,25839,26642,

%U 35456,40081,43680,48203,48762,52554,61760,63665,64232,75140

%N Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.

%C Nelson, Penney, & Pomerance call these "Aaron numbers".

%C 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

%C Number of terms < 10^n: 1, 4, 9, 19, 40, 139, 494, 1748, 6650, ..., . - Robert G. Wilson v, Jan 23 2012.

%D John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120-122.

%D Science, vol. 275, p. 759, 1997.

%D P. Hoffman, The Man Who Loved Only Numbers, pp. 179-181, Hyperion, NY 1998.

%D J. Roberts, Lure of Integers, pp. 250, MAA 1992.

%D D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 159-160, Penguin 1986.

%H Robert G. Wilson v, <a href="/A006145/b006145.txt">Table of n, a(n) for n = 1..6651</a>

%H Joe K. Crump, <a href="http://www.immortaltheory.com/NumberTheory/default.asp?SubPage=RuthAaron.htm">Ruth-Aaron Pairs-an algorithm</a>

%H C. Nelson, D. E. Penney and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/714and715.pdf">714 and 715</a>, J. Recreational Math. 7:2 (1994), pp. 87-89.

%H Ivars Petersen, <a href="http://www.maa.org/mathland/mathland_6_30.html">Related page</a>

%H T. Trotter, Jr., <a href="http://www.trottermath.net/numthry/rutharon.html">Ruth-Aaron Numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ruth-AaronPair.html">Ruth-Aaron Pair</a>

%p with(numtheory): for n from 1 to 10000 do t0 := 0; t1 := factorset(n);

%p for j from 1 to nops(t1) do t0 := t0+t1[ j ]; od: s[ n ] := t0; od:

%p for n from 1 to 9999 do if s[ n ] = s[ n+1 ] then lprint(n,s[ n ]); fi; od:

%t fQ[n_] := Plus @@ (First@# & /@ FactorInteger[n]) == Plus @@ (First@# & /@ FactorInteger[n + 1]); Select[ Range@ 100000, fQ] (* Robert G. Wilson v, Jan 22 2012 *)

%o (PARI) sopf(n)=my(f=factor(n));sum(i=1,#f[,1],f[i,1])

%o is(n)=sopf(n)==sopf(n+1) \\ _Charles R Greathouse IV_, Jan 27 2012

%Y Cf. A006146, A039752, A039753, A054378.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

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