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)).

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

Author

Leroy Quet, Apr 07 2008

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A139082, A139083.

Programs

Mathematica

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 *)

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). [From Franklin T. Adams-Watters, Apr 09 2009]

Extensions

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