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A006145
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Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.
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19
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5, 24, 49, 77, 104, 153, 369, 492, 714, 1682, 2107, 2299, 2600, 2783, 5405, 6556, 6811, 8855, 9800, 12726, 13775, 18655, 21183, 24024, 24432, 24880, 25839, 26642, 35456, 40081, 43680, 48203, 48762, 52554, 61760, 63665, 64232, 75140
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
Number of terms < 10^n: 1, 4, 9, 19, 40, 139, 494, 1748, 6650, ..., . - Robert G. Wilson v, Jan 23 2012.
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REFERENCES
| John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120-122.
C. Nelson, D. E. Penney and C. Pomerance, "714 and 715", J. Recreational Math. 7 (No. 2) 1994, 87-89.
Science, vol. 275, p. 759, 1997.
P. Hoffman, The Man Who Loved Only Numbers, pp. 179-181, Hyperion, NY 1998.
J. Roberts, Lure of Integers, pp. 250, MAA 1992.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 159-160, Penguin 1986.
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 1..6651
Joe K. Crump, Ruth-Aaron Pairs-an algorithm
Ivars Petersen, Related page
T. Trotter, Jr., Ruth-Aaron Numbers
Eric Weisstein's World of Mathematics, Ruth-Aaron Pair
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MAPLE
| with(numtheory): for n from 1 to 10000 do t0 := 0; t1 := factorset(n);
for j from 1 to nops(t1) do t0 := t0+t1[ j ]; od: s[ n ] := t0; od:
for n from 1 to 9999 do if s[ n ] = s[ n+1 ] then lprint(n, s[ n ]); fi; od:
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MATHEMATICA
| fQ[n_] := Plus @@ (First@# & /@ FactorInteger[n]) == Plus @@ (First@# & /@ FactorInteger[n + 1]); Select[ Range@ 100000, fQ] (* Robert G. Wilson v, Jan 22 2012 *)
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PROG
| (PARI) sopf(n)=my(f=factor(n)); sum(i=1, #f[, 1], f[i, 1])
is(n)=sopf(n)==sopf(n+1) \\ Charles R Greathouse IV, Jan 27 2012
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CROSSREFS
| Cf. A006146, A039752, A039753, A054378.
Sequence in context: A056234 A030766 A063143 * A202326 A085646 A121546
Adjacent sequences: A006142 A006143 A006144 * A006146 A006147 A006148
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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