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 A137826 Least prime number that produces the highest abundancy number when multiplied by the product of all previous n-1 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)