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

1,1

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A085072, A085876.

Sequence in context: A251103 A065559 A087317 * A015886 A255354 A344349

Adjacent sequences: A086486 A086487 A086488 * A086490 A086491 A086492

Keyword

nonn

Author

Amarnath Murthy, Jul 28 2003

Extensions

More terms from David Wasserman, Mar 09 2005

Status

approved