cp's OEIS Frontend

A340608 The number of prime factors of n (A001222) is relatively prime to the maximum prime index of n (A061395).

%I A340608 #11 Feb 07 2021 06:25:34
%S A340608 2,3,4,5,7,8,10,11,12,13,15,16,17,18,19,22,23,25,27,28,29,31,32,33,34,
%T A340608 37,40,41,42,43,44,46,47,48,51,53,55,59,60,61,62,63,64,66,67,68,69,70,
%U A340608 71,72,73,76,77,79,80,82,83,85,88,89,90,93,94,97,98,99
%N A340608 The number of prime factors of n (A001222) is relatively prime to the maximum prime index of n (A061395).
%C A340608 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%H A340608 Amiram Eldar, <a href="/A340608/b340608.txt">Table of n, a(n) for n = 1..10000</a>
%e A340608 The sequence of terms together with their prime indices begins:
%e A340608      2: {1}          22: {1,5}          44: {1,1,5}
%e A340608      3: {2}          23: {9}            46: {1,9}
%e A340608      4: {1,1}        25: {3,3}          47: {15}
%e A340608      5: {3}          27: {2,2,2}        48: {1,1,1,1,2}
%e A340608      7: {4}          28: {1,1,4}        51: {2,7}
%e A340608      8: {1,1,1}      29: {10}           53: {16}
%e A340608     10: {1,3}        31: {11}           55: {3,5}
%e A340608     11: {5}          32: {1,1,1,1,1}    59: {17}
%e A340608     12: {1,1,2}      33: {2,5}          60: {1,1,2,3}
%e A340608     13: {6}          34: {1,7}          61: {18}
%e A340608     15: {2,3}        37: {12}           62: {1,11}
%e A340608     16: {1,1,1,1}    40: {1,1,1,3}      63: {2,2,4}
%e A340608     17: {7}          41: {13}           64: {1,1,1,1,1,1}
%e A340608     18: {1,2,2}      42: {1,2,4}        66: {1,2,5}
%e A340608     19: {8}          43: {14}           67: {19}
%t A340608 Select[Range[100],GCD[PrimeOmega[#],PrimePi[FactorInteger[#][[-1,1]]]]==1&]
%Y A340608 Note: Heinz numbers are given in parentheses below.
%Y A340608 These are the Heinz numbers of the partitions counted by A200750.
%Y A340608 The case of equality is A047993 (A106529).
%Y A340608 The divisible instead of coprime version is A168659 (A340609).
%Y A340608 The dividing instead of coprime version is A168659 (A340610), with strict case A340828 (A340856).
%Y A340608 A001222 counts prime factors.
%Y A340608 A006141 counts partitions whose length equals their minimum (A324522).
%Y A340608 A051424 counts singleton or pairwise coprime partitions (A302569).
%Y A340608 A056239 adds up prime indices.
%Y A340608 A061395 selects the maximum prime index.
%Y A340608 A067538 counts partitions whose length divides their sum (A316413).
%Y A340608 A067538 counts partitions whose maximum divides their sum (A326836).
%Y A340608 A112798 lists the prime indices of each positive integer.
%Y A340608 A259936 counts singleton or pairwise coprime factorizations.
%Y A340608 A325134 = A001222 + A061395.
%Y A340608 A326845 = A056239 * A061395.
%Y A340608 A326849 counts partitions whose sum divides length times maximum (A326848).
%Y A340608 A327516 counts pairwise coprime partitions (A302696).
%Y A340608 Cf. A003114, A039900, A096401, A244990/A244991, A340606, A340653, A340691, A340787/A340788.
%K A340608 nonn
%O A340608 1,1
%A A340608 _Gus Wiseman_, Jan 27 2021