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

1,1

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

Table of n, a(n) for n=1..66.

Formula

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

Prog

Contribution from Franklin T. Adams-Watters, Apr 09 2009: (Start)
(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<r, r=pp)); r)
vector(80, i, minpp(i)*minpp(i+1)) (End)

Crossrefs

Cf. A139082, A139083.

Sequence in context: A033154 A340663 A354759 * A086958 A130492 A305702

Adjacent sequences: A139081 A139082 A139083 * A139085 A139086 A139087

Keyword

nonn

Author

Leroy Quet, Apr 07 2008

Extensions

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

Status

approved