A137826 Least prime number that produces the highest abundancy number when multiplied by the product of all previous n-1 terms.

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

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: A069227 A117368 A355091 * 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