A086489 Smallest k such that k and k + n have the same prime signature.

2, 3, 2, 3, 2, 5, 14, 3, 2, 3, 2, 5, 21, 3, 2, 3, 2, 5, 8, 3, 2, 7, 10, 5, 10, 3, 2, 3, 2, 7, 15, 5, 6, 3, 2, 5, 14, 3, 2, 3, 2, 5, 14, 3, 2, 7, 10, 5, 6, 3, 2, 6, 21, 5, 10, 3, 2, 3, 2, 7, 21, 5, 6, 3, 2, 5, 10, 3, 2, 3, 2, 7, 14, 5, 10, 3, 2, 5, 6, 3, 2, 7, 10, 5, 6, 3, 2, 6, 6, 7, 15, 5, 22, 3, 2, 5, 14

Offset: 1

Author

Amarnath Murthy, Jul 28 2003

Keywords

• nonn

Examples

			a(7) = 14 as 14 and 14+7 = 21 have the same prime signature p*q.
a(13) = 21 as 21 is the smallest number such that 21 +13 = 34 and 21 both have the same prime signature p*q.
a(19) = 8 as 8 +19 = 27 = 3^3,8 = 2^3 both have the prime signature p^3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A085072, A085876.

Programs

PARI

ps(n) = local(f); f = factor(n); vecsort(f[,2]); a(n) = local(P, m, v); P = vector(n, i, ps(i)); m = 1; while (1, for (i = 1, n, v = ps(m*n + i); if (v == P[i], return((m - 1)*n + i), P[i] = v)); m++); \\ David Wasserman, Mar 09 2005

Extensions

More terms from David Wasserman, Mar 09 2005