A202463 First number of divisor symmetry n: d(n-k) = d(n+k) for 1 <= k <= n, but d(n-k-1) != d(n+k+1).

4, 9, 216, 30, 20376, 432, 18000, 13338864, 15194736, 866452464, 5175273600, 35399473200

Offset

1,1

Comments

3*10^11 < a(13) <= 1245273287760. a(14) = 72462882816. - Donovan Johnson, Dec 25 2011

Links

Table of n, a(n) for n=1..12.

Example

8 and 10 have 4 divisors each, 7 and 11 have 2 divisors each, but 6 and 12 have different numbers of divisors; thus 9 has divisor symmetry 2. Since no smaller number has this, a(2) = 9.

Prog

(PARI) a(n)=my(k=n); while(k++, for(i=1, n, if(numdiv(k-i)!=numdiv(k+i), next(2))); if(numdiv(k-n-1)==numdiv(k+n+1), next); return(k))

Crossrefs

Cf. A093492, A006558.

Sequence in context: A029999 A006280 A290158 * A286322 A318615 A030074

Adjacent sequences: A202460 A202461 A202462 * A202464 A202465 A202466

Keyword

nonn,hard

Author

Charles R Greathouse IV, Dec 19 2011

Extensions

a(11) from Donovan Johnson, Dec 20 2011

a(12) from Donovan Johnson, Dec 25 2011

Status

approved