cp's OEIS Frontend

A091896 Numbers n such that there exists no k for which the denominator of d(k)/k is n, where d = A000005 is the number-of-divisors function.

%I A091896 #27 Apr 17 2022 03:58:54
%S A091896 18,30,72,112,144,243,252,288,294,336,360,396,468,504,576,612,616,625,
%T A091896 684,726,728,792,810,828,840,936,952,960,1014,1044,1064,1116,1224,
%U A091896 1250,1260,1288,1332,1350,1368,1386,1440,1476,1548,1568,1584,1624,1638,1656
%N A091896 Numbers n such that there exists no k for which the denominator of d(k)/k is n, where d = A000005 is the number-of-divisors function.
%C A091896 The number of terms <= 10^n: 0, 3, 28, 311, 3541, for n = 1, 2, 3, 4, 5.
%C A091896 Sequence A353011 lists the indices n such that A090395(k) > A090395(n) for all k > n. This allows one to know whether a given number is in this sequence or not. - _M. F. Hasler_, Apr 15 2022
%C A091896 Another way to confirm a 0 is by looking at A005179(m)/m. If A005179(m)/m > n then d(k) cannot be a multiple of m. - _David A. Corneth_, Apr 16 2022
%H A091896 M. F. Hasler and David A. Corneth, <a href="/A091896/b091896.txt">Table of n, a(n) for n = 1..10000</a> (first 3541 terms from M. F. Hasler)
%t A091896 a = Table[0, {2000}]; Do[m = n; b = Denominator[ DivisorSigma[0, n]/n]; If[b < 2001 && a[[b]] == 0, a[[b]] = n], {n, 1, 25000000}]; Select[ Range[2000], a[[ # ]] == 0 &]
%o A091896 (PARI) select( {is_A091896(n)=!A091895(n)}, [1..10^4] ) \\ _M. F. Hasler_, Apr 04 2022
%Y A091896 Cf. A000005 (number-of-divisors function d), A005179 (smallest number with exactly n divisors), A090395 (denominator of d(n)/n), A353011 (indices of "late birds" in A090395).
%Y A091896 Indices of zeros in A091895 (index where n occurs first in A090395, or 0 if n is not in A090395).
%K A091896 nonn
%O A091896 1,1
%A A091896 _Robert G. Wilson v_, Feb 09 2004
%E A091896 Edited by _M. F. Hasler_, Apr 04 2022