A063274 Number of powerful numbers (definition 1) required to sum to n.

1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 3, 2, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 1, 2, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 3, 2, 1, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 1, 2, 2, 3, 2, 3, 3, 3, 2, 1, 2, 3, 3, 2, 3, 4, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 1, 2, 3, 3, 2, 3

Offset

1,2

Comments

Heath-Brown proves that a(n) <= 3 for all large n. It seems that n > 119 suffices. - Charles R Greathouse IV, Nov 19 2012

References

D. R. Heath-Brown, Ternary quadratic forms and sums of three square-full numbers, Séminaire de Théorie des Nombres, Paris 1986-87, pp. 137-163; Progr. Math., 75, Birkhäuser Boston, Boston, MA, 1988.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

The powerful numbers (A001694) start 1,4,8,9,... 11=1+1+9 and is not the sum of fewer terms, so a(11)=3.

Prog

(PARI) W=vector(99); W[1]=1; for(n=2, #W, if(ispowerful(n), W[n]=1; next); b=n; for(i=1, n\2, b=min(b, W[i]+W[n-i])); W[n]=b); W \\ Charles R Greathouse IV, Nov 19 2012

Crossrefs

Cf. A001694, A056828, A063275.

Sequence in context: A065365 A096137 A282905 * A274459 A225926 A354761

Adjacent sequences: A063271 A063272 A063273 * A063275 A063276 A063277

Keyword

nonn

Author

Jud McCranie, Jul 13 2001

Status

approved