A139083 -id:A139083 - cp's OEIS frontend

A139081 a(n) = (largest prime power dividing n) + (largest prime power dividing (n+1)).

3, 5, 7, 9, 8, 10, 15, 17, 14, 16, 15, 17, 20, 12, 21, 33, 26, 28, 24, 12, 18, 34, 31, 33, 38, 40, 34, 36, 34, 36, 63, 43, 28, 24, 16, 46, 56, 32, 21, 49, 48, 50, 54, 20, 32, 70, 63, 65, 74, 42, 30, 66, 80, 38, 19, 27, 48, 88, 64, 66, 92, 40, 73, 77, 24, 78, 84, 40, 30

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 = 17.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A139082, A139083.

With[{c=Table[Max[#[[1]]^#[[2]]&/@FactorInteger[n]],{n,70}]},Total/@ Partition[ c,2,1]] (* Harvey P. Dale, Nov 18 2014 *)

maxpp(n)=local(m,r,pp);m=factor(n);r=1;for(i=1,matsize(m)[1],pp=m[i,1]^m[i,2];if(pp>r,r=pp));r
vector(80,i,maxpp(i)+maxpp(i+1)) (End)

a(n) = A034699(n) + A034699(n+1). [From Franklin T. Adams-Watters, Apr 09 2009]

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

Definition clarified by Harvey P. Dale, Nov 18 2014

A139084 a(n) = (smallest prime-power among the largest powers dividing n of each prime dividing n) * (smallest prime-power among the largest powers dividing (n+1) of each prime dividing (n+1)).

Original entry on oeis.org

2, 6, 12, 20, 10, 14, 56, 72, 18, 22, 33, 39, 26, 6, 48, 272, 34, 38, 76, 12, 6, 46, 69, 75, 50, 54, 108, 116, 58, 62, 992, 96, 6, 10, 20, 148, 74, 6, 15, 205, 82, 86, 172, 20, 10, 94, 141, 147, 98, 6, 12, 212, 106, 10, 35, 21, 6, 118, 177, 183, 122, 14, 448, 320, 10, 134

Offset: 1

Leroy Quet, Apr 07 2008

nonn

The largest powers dividing 44 of each prime dividing 44 are 2^2 and 11^1. The least of these is 2^2 =4. The largest powers dividing 45 of each prime dividing 45 are 3^2 and 5^1. The least of these is 5^1 = 5. So a(44) = 4 * 5 = 20.

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

Cf. A139082, A139083.

f[{a_,b_}]:=a^b;a[n_]:=Min[f/@FactorInteger[n]]*Min[f/@FactorInteger[n+1]];Array[a,66] (* 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). [From Franklin T. Adams-Watters, Apr 09 2009]

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

cp's OEIS Frontend

A139081 a(n) = (largest prime power dividing n) + (largest prime power dividing (n+1)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions