

A137826


Least prime number that produces the highest abundancy number when multiplied by the product of all previous n1 terms.


2



2, 3, 5, 2, 7, 11, 3, 13, 2, 17, 19, 23, 29, 2, 5, 31, 37, 3, 41, 43, 47, 53, 7, 59, 61, 2, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 3, 2, 127, 131, 11, 137, 139, 149, 151, 5, 157, 163, 167, 173, 179, 181, 13, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241
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OFFSET

1,1


COMMENTS

"Least" is required in the definition, otherwise a(14) could be either 2 or 5 because 2*77636318760 and 5*77636318760 have the same abundancy. It appears that only a(14) has this property.  T. D. Noe, Jan 24 2010


LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
The Prime Glossary, Abundant Numbers.
Eric Weisstein's World of Mathematics, Abundancy.


EXAMPLE

a(4)=2 since the product a(1)*a(2)*a(3) is 2*3*5=30, and
30*2 = 60 has abundancy 2.8, whereas
30*3 = 90 has abundancy 2.6,
30*5 = 150 has abundancy 2.48,
30*7 = 210 has abundancy 2.7428571..., etc.


MATHEMATICA

Abundancy[k_Integer] := DivisorSigma[1, k]/k; SetAttributes[Abundancy, Listable]; nn=100; lastPrime=1; n=1; Table[a=Abundancy[n*Prime[Range[lastPrime+1]]]; pos=Position[a, Max[a]]; p=Prime[pos[[1, 1]]]; If[pos[[1, 1]>lastPrime, lastPrime++ ]; n=n*p; p, {nn}] (* T. D. Noe, Jan 24 2010 *)


CROSSREFS

Cf. A005101, A017665, A017666, A137825 (product of terms).
Sequence in context: A224382 A069227 A117368 * A021429 A262217 A124055
Adjacent sequences: A137823 A137824 A137825 * A137827 A137828 A137829


KEYWORD

easy,nonn


AUTHOR

Sergio Pimentel, Feb 11 2008


EXTENSIONS

Edited by T. D. Noe, Jan 24 2010
Extended by T. D. Noe, Jan 24 2010
Edited by Jon E. Schoenfield, Mar 02 2019


STATUS

approved



