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A006145 Ruth-Aaron 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Nelson, Penney, & Pomerance call these "Aaron numbers" 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), 120-122.

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.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..6651

Joe K. Crump, Ruth-Aaron Pairs-an algorithm

Brady Haran and Carl Pomerance, Aaron Numbers - Numberphile (2017)

G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonné, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74. (Annotated scanned copy)

C. Nelson, D. E. Penney and C. Pomerance, 714 and 715, J. Recreational Math. 7:2 (1994), pp. 87-89.

Ivars Peterson, Playing with Ruth-Aaron pairs

T. Trotter, Jr., Ruth-Aaron Numbers [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]

Eric Weisstein's World of Mathematics, Ruth-Aaron 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

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Last modified May 21 15:08 EDT 2018. Contains 304397 sequences. (Running on oeis4.)