A139084 -id:A139084 - cp's OEIS frontend

A139082 a(n) = (largest power of a prime dividing n) * (largest power of a prime dividing (n+1)).

2, 6, 12, 20, 15, 21, 56, 72, 45, 55, 44, 52, 91, 35, 80, 272, 153, 171, 95, 35, 77, 253, 184, 200, 325, 351, 189, 203, 145, 155, 992, 352, 187, 119, 63, 333, 703, 247, 104, 328, 287, 301, 473, 99, 207, 1081, 752, 784, 1225, 425, 221, 689, 1431, 297, 88, 152, 551

Offset: 1

Leroy Quet, Apr 07 2008

nonn

The largest prime-power dividing 12 is 4. The largest prime power dividing 13 is 13. So a(12) = 4*13 = 52.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A139081, A139084.

isA000961 := proc(n) if nops(ifactors(n)[2]) =1 then true ; else false ; fi ; end: A034699 := proc(n) local dvs,d ; if n = 1 then RETURN(1) ; fi ; dvs := sort(convert(numtheory[divisors](n),list),`>`) ; for d in dvs do if isA000961(d) then RETURN(d) ; fi ; od: RETURN(0) ; end: A139082 := proc(n) A034699(n)*A034699(n+1) ; end: seq(A139082(n),n=1..100) ; # R. J. Mathar, Apr 16 2008

Times @@ # & /@ Partition[Array[Max@ Map[Power @@ # &, FactorInteger@ #] &, 58], 2, 1] (* Michael De Vlieger, Oct 22 2017 *)

a(n) = A034699(n)*A034699(n+1). - R. J. Mathar, Apr 16 2008

More terms from R. J. Mathar, Apr 16 2008

A139083 a(n) = (smallest prime-power among the largest powers of each prime dividing n) + (smallest prime-power among the largest powers of each prime dividing (n+1)).

Original entry on oeis.org

3, 5, 7, 9, 7, 9, 15, 17, 11, 13, 14, 16, 15, 5, 19, 33, 19, 21, 23, 7, 5, 25, 26, 28, 27, 29, 31, 33, 31, 33, 63, 35, 5, 7, 9, 41, 39, 5, 8, 46, 43, 45, 47, 9, 7, 49, 50, 52, 51, 5, 7, 57, 55, 7, 12, 10, 5, 61, 62, 64, 63, 9, 71, 69, 7, 69, 71, 7, 5, 73, 79, 81, 75, 5, 7, 11, 9, 81

Offset: 1

Leroy Quet, Apr 07 2008

nonn

The largest powers of each prime dividing 44 are 2^2 and 11^1. The least of these is 2^2 =4. The largest powers of each prime dividing 45 are 3^2 and 5^1. The least of these is 5^1 = 5. So a(44) = 4 + 5 = 9.

Cf. A139081, A139084.

f[{a_,b_}]:=a^b;a[n_]:=Min[f/@FactorInteger[n]]+Min[f/@FactorInteger[n+1]];Array[a,78] (* James C. McMahon, Jun 28 2025 *)

minpp(n)=local(m,r,pp);if(n==1,1,m=factor(n);r=m[1,1]^m[1,2];for(i=2,matsize(m)[1],pp=m[i,1]^m[i,2];if(pp

a(n) = A034684(n) + A034684(n+1). [Franklin T. Adams-Watters, Apr 09 2009]

More terms from Franklin T. Adams-Watters, Apr 09 2009

cp's OEIS Frontend

A139082 a(n) = (largest power of a prime dividing n) * (largest power of a prime dividing (n+1)).

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