

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 ith smallest divisor of n and d(n) denotes the number of divisors of n (A000005).


5



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
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OFFSET

1,2


COMMENTS

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


LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



