A087990 Number of palindromic divisors of n.

1, 2, 2, 3, 2, 4, 2, 4, 3, 3, 2, 5, 1, 3, 3, 4, 1, 5, 1, 4, 3, 4, 1, 6, 2, 2, 3, 4, 1, 5, 1, 4, 4, 2, 3, 6, 1, 2, 2, 5, 1, 5, 1, 6, 4, 2, 1, 6, 2, 3, 2, 3, 1, 5, 4, 5, 2, 2, 1, 6, 1, 2, 4, 4, 2, 8, 1, 3, 2, 4, 1, 7, 1, 2, 3, 3, 4, 4, 1, 5, 3, 2, 1, 6, 2, 2, 2, 8, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 6, 4, 2, 4, 1, 4, 4

Offset

1,2

Links

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

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A118031 = 3.370283... . - Amiram Eldar, Jan 01 2024

Example

n=132: divisors={1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132}, revdivisors={1, 2, 3, 4, 6, 11, 21, 22, 33, 44, 66, 231}, a[132]=10; so 10 of 12 divisors of n are palindromic: {1, 2, 3, 4, 6, 11, 22, 33, 44, 66}.

Mathematica

nd[x_, y_] := 10*x+y; tn[x_] := Fold[nd, 0, x]; rdi[x_] := tn[Reverse[IntegerDigits[x]]]; d0[x_] := DivisorSigma[0, x]; di[x_, i_] := Part[Divisors[x], i]; Table[Count[Divisors[s]-Table[rdi[di[s, w]], {w, 1, d0[s]}], 0], {s, 1, 256}]
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; Table[Count[Divisors[n], _?(palQ[#] &)], {n, 105}] (* Jayanta Basu, Aug 10 2013 *)
Table[Count[Divisors[n], _?PalindromeQ], {n, 110}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 28 2017 *)

Prog

(Python)
def ispal(n):
    t = str(n)
    return t == t[::-1]
def A087990(n):
    s=0
    for i in range(1, n+1):
        if n%i==0 and ispal(i):
            s+=1
    return s # Indranil Ghosh, Feb 10 2017
(PARI) a(n) = sumdiv(n, d, my(dd=digits(d)); Vecrev(dd) == dd); \\ Michel Marcus, Apr 06 2020

Crossrefs

Cf. A062687, A087991, A088000, A118031.

Sequence in context: A076888 A357171 A355698 * A335037 A356069 A179940

Adjacent sequences: A087987 A087988 A087989 * A087991 A087992 A087993

Keyword

nonn,base

Author

Labos Elemer, Oct 08 2003

Status

approved