

A069248


Number of positive divisors of n themselves divisible by largest prime that divides n.


1



0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 4, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 4, 1, 5, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 2, 4, 2, 3, 1, 6, 2, 4, 2, 2, 1, 6, 1, 2, 3, 6, 2, 4, 1, 3, 2, 4, 1, 8, 1, 2, 4, 3, 2, 4, 1, 5, 4, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 4, 3, 6
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OFFSET

1,4


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..10000


FORMULA

d(n) E_n/(E_n + 1), where d(n) is the number of positive divisors of n and E_n is the exponent of the largest prime to divide n in the prime factorization of n.


EXAMPLE

The divisors of 12 which are themselves divisible by 3 (the largest prime dividing 12) are 3, 6 and 12. So the 12th term is 3.


MATHEMATICA

nd[n_]:=Module[{lp=FactorInteger[n][[1, 1]]}, Count[Divisors[n], _?(Mod[ #, lp] == 0&)]]; Join[{0}, Array[nd, 100, 2]] (* Harvey P. Dale, May 05 2019 *)


PROG

(PARI) a(n) = if (n==1, 0, gp = vecmax(factor(n)[, 1]); sumdiv(n, d, ((d%gp) == 0))); \\ Michel Marcus, Feb 10 2017


CROSSREFS

Sequence in context: A324190 A098893 A302037 * A329378 A329617 A008481
Adjacent sequences: A069245 A069246 A069247 * A069249 A069250 A069251


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 08 2002


STATUS

approved



