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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.
6
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
1,1
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)
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 &]
PROG
(PARI) select( {is_A091896(n)=!A091895(n)}, [1..10^4] ) \\ M. F. Hasler, Apr 04 2022
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).
Sequence in context: A043143 A043923 A160916 * A101140 A287683 A182254
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Feb 09 2004
EXTENSIONS
Edited by M. F. Hasler, Apr 04 2022
STATUS
approved