A322586 a(n) = 1 if n is a highly composite number (A002182), 0 otherwise.

1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1

Comments

Characteristic function of A002182, first differences of A261100, Möbius transform of A181801.

Links

Antti Karttunen, Table of n, a(n) for n = 1..83160

Index entries for characteristic functions

Formula

a(1) = 1; for n > 1, a(n) = A261100(n) - A261100(n-1).

For all n, a(n) <= A322585(n).

Prog

(PARI)
v002182 = vector(128); v002182[1] = 1; \\ For memoization.
A002182(n) = { my(d, k); if(v002182[n], v002182[n], k = A002182(n-1); d = numdiv(k); while(numdiv(k) <= d, k=k+1); v002182[n] = k; k); };
A261100(n) = { my(k=1); while(A002182(k)<=n, k=k+1); (k-1); };
A322586(n) = if(1==n, 1, (A261100(n)-A261100(n-1)));

Crossrefs

Cf. A002182, A181801, A261100 (partial sums), A322585.

Sequence in context: A167501 A285533 A185175 * A147612 A323509 A197183

Adjacent sequences: A322583 A322584 A322585 * A322587 A322588 A322589

Keyword

nonn

Author

Antti Karttunen, Dec 20 2018

Status

approved