

A248955


Number of polynomials a_k*x^k + ... + a_1*x + n with k > 0, integer coefficients and distinct positive integer roots and positive integers n.


3



1, 3, 3, 5, 3, 9, 3, 9, 5, 9, 3, 17, 3, 9, 9, 13, 3, 17, 3, 17, 9, 9, 3, 31, 5, 9, 9, 17, 3, 29, 3, 19, 9, 9, 9, 35, 3, 9, 9, 31, 3, 29, 3, 17, 17, 9, 3, 49, 5, 17, 9, 17, 3, 31, 9, 31, 9, 9, 3, 61, 3, 9, 17, 27, 9, 29, 3, 17, 9, 29, 3, 67, 3, 9, 17, 17, 9
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OFFSET

1,2


COMMENTS

If D_n is the set of all positive divisors of n, then a(n) gives the number of all subsets of D_n for which the product of all their elements is a divisor of n. a(n) depends only on the prime signature of n.


LINKS



FORMULA



EXAMPLE

a(2) = 3: 2x+2; x+2; x^2  3x + 2.


PROG

(PARI) padbin(n, len) = {b = binary(n); while(length(b) < len, b = concat(0, b); ); b; }
a(n) = {d = divisors(n); nbd = #d; nbts = 2^nbd1; nbs = 0; for (i=1, nbts, bin = padbin(i, nbd); prd = prod(j=1, nbd, if (bin[j], d[j], 1)); if (n % prd == 0, nbs++); ); nbs; } \\ Michel Marcus, Nov 07 2014


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



