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

Author

Leroy Quet, Apr 07 2008

Keywords

• nonn

Comments

The largest prime-power dividing 12 is 4. The largest prime power dividing 13 is 13. So a(12) = 4+13 = 17.

Links

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

Crossrefs

Cf. A139082, A139083.

Programs

Mathematica

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

PARI

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)

Formula

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

Extensions

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

Definition clarified by Harvey P. Dale, Nov 18 2014