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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 (list; graph; refs; listen; history; text; internal format)
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: A029620 A204100 A048691 * A071053 A298398 A094439

Adjacent sequences:  A248952 A248953 A248954 * A248956 A248957 A248958

KEYWORD

nonn

AUTHOR

Reiner Moewald, Oct 17 2014

STATUS

approved

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)