A141286 a(n) = the smallest positive multiple of n such that a(n) is divisible by A001222(a(n)), where A001222(m) is the sum of the exponents in the prime factorization of m.

2, 2, 3, 4, 5, 6, 7, 16, 18, 10, 11, 12, 13, 14, 30, 16, 17, 18, 19, 40, 42, 22, 23, 24, 75, 26, 27, 56, 29, 30, 31, 96, 66, 34, 105, 36, 37, 38, 78, 40, 41, 42, 43, 88, 45, 46, 47, 96, 147, 100, 102, 104, 53, 216, 165, 56, 114, 58, 59, 60, 61, 62, 63, 256, 195, 66, 67, 136, 138

Offset

1,1

Links

Table of n, a(n) for n=1..69.

Example

For n = 25, checking: 1*25 = 25 = 5^2. The sum of the exponents in the prime-factorization of 5^2 is 2. 2 does not divide 25. 2*25 = 50 = 2^1 *5^2. The sum of the exponents is 1+2=3. 3 does not divide 50. 3*25 = 75 = 3^1 *5^2. The sum of the exponents is 3. Now, 3 does divide 75. So a(25) = 75.

Maple

A001222 := proc(n) numtheory[bigomega](n) ; end: A141286 := proc(n) local k ; for k from 1 do if k*n > 1 then if (k*n) mod A001222(k*n) = 0 then RETURN( k*n ) ; fi; fi; od: end: seq(A141286(n), n=1..80) ; # R. J. Mathar, Feb 19 2009

Crossrefs

Cf. A001222.

Sequence in context: A370808 A111212 A338317 * A165686 A025209 A125573

Adjacent sequences: A141283 A141284 A141285 * A141287 A141288 A141289

Keyword

nonn

Author

Leroy Quet, Aug 01 2008

Extensions

More terms from R. J. Mathar, Feb 19 2009

Status

approved