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.

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

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

Reiner Moewald, Table of n, a(n) for n = 1..2159

Formula

a(p) = 3, for p prime. - Michel Marcus, Nov 07 2014

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^nbd-1; 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

Cf. A248410, A248956.

Sequence in context: A204100 A048691 A332730 * A071053 A298398 A376691

Adjacent sequences: A248952 A248953 A248954 * A248956 A248957 A248958

Keyword

nonn

Author

Reiner Moewald, Oct 17 2014

Status

approved