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)).

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

Author

Leroy Quet, Apr 07 2008

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A139081, A139084.

Programs

Mathematica

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 *)

PARI

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
				

Formula

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

Extensions

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