A137849 Number of integers m from 1 through n inclusive such that d_i(n)<=d_i(m) for 1<=i<=Min(d(n),d(m)) where d_i(n) denotes the i-th smallest divisor of n and d(n) denotes the number of divisors of n (A000005).

1, 2, 2, 4, 2, 6, 2, 7, 5, 7, 2, 12, 2, 9, 8, 14, 2, 17, 2, 17, 10, 10, 2, 24, 9, 12, 12, 23, 2, 28, 2, 25, 13, 14, 12, 35, 2, 15, 14, 34, 2, 36, 2, 30, 23, 17, 2, 48, 14, 33, 18, 34, 2, 46, 18, 45, 19, 19, 2, 60, 2, 21, 30, 49, 20, 54, 2, 41, 22, 47, 2, 71, 2, 24, 36, 45, 21, 63, 2, 67

Offset

1,2

Comments

In other words, number of integers m in {1,...,n} such that the i-th divisor of m is >= the i-th divisor of n, for i=1,...,min(A000005(m),A000005(n)).

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000.

Formula

a(n) = 2 iff n is prime.

Example

a(10) = 7 because there are 7 integers, 1, 2, 3, 5, 7, 9 and 10, whose divisors meet the criterion for n = 10 (4 does not meet this criterion in that 4's 3rd smallest divisor is 4 and 10's third smallest divisor is 5; similarly 6 and 8 do not meet the criterion).

Mathematica

f[n_] := Block[{c = 1, d = Divisors@ n, k = DivisorSigma[0, n], m = 1}, While[m != n, If[ Min[ PadRight[ Divisors@ m, k, n] - d] > -1, c++ ]; m++ ]; c]; Array[f, 80] (* Robert G. Wilson v *)

Prog

(PARI) A137849(n)={ local( d=divisors(n), d2 ); sum( m=1, n, d2=divisors(m); vecmin( vector(min(#d, #d2), i, d2[i]-d[i]))>=0 )} \\ - M. F. Hasler, May 01 2008

Crossrefs

Cf. A094783 (numbers where a(n) = n), Records: A140067.

Sequence in context: A121599 A360593 A080221 * A316440 A118982 A129457

Adjacent sequences: A137846 A137847 A137848 * A137850 A137851 A137852

Keyword

nonn

Author

J. Lowell, Apr 29 2008

Extensions

Edited and extended by M. F. Hasler and Ray Chandler, May 01 2008

Status

approved