

A006145


RuthAaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.


24



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
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OFFSET

1,1


COMMENTS

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


REFERENCES

John L. Drost, Ruth/Aaron Pairs, J. Recreational Math. 28 (No. 2), 120122.
Science, vol. 275, p. 759, 1997.
P. Hoffman, The Man Who Loved Only Numbers, pp. 179181, Hyperion, NY 1998.
J. Roberts, Lure of Integers, pp. 250, MAA 1992.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 159160, Penguin 1986.


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..6651
Joe K. Crump, RuthAaron Pairsan algorithm
C. Nelson, D. E. Penney and C. Pomerance, 714 and 715, J. Recreational Math. 7:2 (1994), pp. 8789.
Ivars Petersen, Related page
T. Trotter, Jr., RuthAaron Numbers
Eric Weisstein's World of Mathematics, RuthAaron Pair


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:


MATHEMATICA

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


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


CROSSREFS

Cf. A006146, A039752, A039753, A054378.
Sequence in context: A056234 A030766 A063143 * A219509 A202326 A085646
Adjacent sequences: A006142 A006143 A006144 * A006146 A006147 A006148


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


STATUS

approved



