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.

18, 30, 72, 112, 144, 243, 252, 288, 294, 336, 360, 396, 468, 504, 576, 612, 616, 625, 684, 726, 728, 792, 810, 828, 840, 936, 952, 960, 1014, 1044, 1064, 1116, 1224, 1250, 1260, 1288, 1332, 1350, 1368, 1386, 1440, 1476, 1548, 1568, 1584, 1624, 1638, 1656

Offset: 1

Author

Robert G. Wilson v, Feb 09 2004

Keywords

• nonn

Comments

The number of terms <= 10^n: 0, 3, 28, 311, 3541, for n = 1, 2, 3, 4, 5.

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

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

Links

• M. F. Hasler and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3541 terms from M. F. Hasler)

Crossrefs

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).

Indices of zeros in A091895 (index where n occurs first in A090395, or 0 if n is not in A090395).

Programs

Mathematica

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 &]

PARI

select( {is_A091896(n)=!A091895(n)}, [1..10^4] ) \\ M. F. Hasler, Apr 04 2022

Extensions

Edited by M. F. Hasler, Apr 04 2022