# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a341642 Showing 1-1 of 1 %I A341642 #11 Nov 01 2024 05:15:59 %S A341642 0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,1,0,1,1, %T A341642 1,0,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,1, %U A341642 1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,1,1 %N A341642 Number of strictly superior prime divisors of n. %C A341642 We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673. %C A341642 All terms are binary numbers. %H A341642 Amiram Eldar, Table of n, a(n) for n = 1..10000 %e A341642 The sequence of sets of strictly superior prime divisors of each positive integer begins: {}, {2}, {3}, {}, {5}, {3}, {7}, {}, {}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {5}, ... %t A341642 Table[Length[Select[Divisors[n],PrimeQ[#]&>n/#&]],{n,100}] %t A341642 a[n_] := Count[FactorInteger[n][[;; , 1]], _?(#^2 > n &)]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Nov 01 2024 *) %o A341642 (PARI) a(n) = #select(x -> (x^2 > n), factor(n)[, 1]); \\ _Amiram Eldar_, Nov 01 2024 %Y A341642 Positions of zeros are A048098. %Y A341642 The inferior version is A063962. %Y A341642 Positions of ones are A064052. %Y A341642 The strictly inferior version is A333806. %Y A341642 Dominated by A341591 (the weak version). %Y A341642 The version for odd instead of prime divisors is A341594. %Y A341642 The version for squarefree instead of prime divisors is A341595. %Y A341642 The strictly superior prime divisors themselves are listed by A341643. %Y A341642 The version for prime-power instead of prime divisors is A341644. %Y A341642 A001221 counts prime divisors, with sum A001414. %Y A341642 A140271 selects the smallest strictly superior divisor. %Y A341642 A038548 counts superior (or inferior) divisors. %Y A341642 A056924 counts strictly superior (or strictly inferior) divisors. %Y A341642 A207375 list central divisors. %Y A341642 A341673 lists strictly superior divisors. %Y A341642 - Inferior: A033676, A066839, A069288, A161906, A217581, A333749, A333750. %Y A341642 - Superior: A033677, A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341592, A341593, A341675, A341676. %Y A341642 - Strictly Inferior: A060775, A333805, A341596, A341674. %Y A341642 - Strictly Superior: A238535, A341644, A341646. %Y A341642 Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798. %K A341642 nonn %O A341642 1 %A A341642 _Gus Wiseman_, Feb 21 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE