cp's OEIS Frontend

A340856 Squarefree numbers whose greatest prime index (A061395) is divisible by their number of prime factors (A001222).

%I A340856 #10 Feb 07 2021 19:43:27
%S A340856 2,3,5,6,7,11,13,14,17,19,21,23,26,29,30,31,35,37,38,39,41,43,47,53,
%T A340856 57,58,59,61,65,67,71,73,74,78,79,83,86,87,89,91,95,97,101,103,106,
%U A340856 107,109,111,113,122,127,129,130,131,133,137,138,139,142,143,145
%N A340856 Squarefree numbers whose greatest prime index (A061395) is divisible by their number of prime factors (A001222).
%C A340856 Also Heinz numbers of strict integer partitions whose greatest part is divisible by their number of parts. These partitions are counted by A340828.
%e A340856 The sequence of terms together with their prime indices begins:
%e A340856       2: {1}         31: {11}       71: {20}
%e A340856       3: {2}         35: {3,4}      73: {21}
%e A340856       5: {3}         37: {12}       74: {1,12}
%e A340856       6: {1,2}       38: {1,8}      78: {1,2,6}
%e A340856       7: {4}         39: {2,6}      79: {22}
%e A340856      11: {5}         41: {13}       83: {23}
%e A340856      13: {6}         43: {14}       86: {1,14}
%e A340856      14: {1,4}       47: {15}       87: {2,10}
%e A340856      17: {7}         53: {16}       89: {24}
%e A340856      19: {8}         57: {2,8}      91: {4,6}
%e A340856      21: {2,4}       58: {1,10}     95: {3,8}
%e A340856      23: {9}         59: {17}       97: {25}
%e A340856      26: {1,6}       61: {18}      101: {26}
%e A340856      29: {10}        65: {3,6}     103: {27}
%e A340856      30: {1,2,3}     67: {19}      106: {1,16}
%t A340856 Select[Range[2,100],SquareFreeQ[#]&&Divisible[PrimePi[FactorInteger[#][[-1,1]]],PrimeOmega[#]]&]
%Y A340856 Note: Heinz number sequences are given in parentheses below.
%Y A340856 The case of equality, and the reciprocal version, are both A002110.
%Y A340856 The non-strict reciprocal version is A168659 (A340609).
%Y A340856 The non-strict version is A168659 (A340610).
%Y A340856 These are the Heinz numbers of partitions counted by A340828.
%Y A340856 A001222 counts prime factors.
%Y A340856 A006141 counts partitions whose length equals their minimum (A324522).
%Y A340856 A056239 adds up the prime indices.
%Y A340856 A061395 selects the maximum prime index.
%Y A340856 A067538 counts partitions whose length divides their sum (A316413/A326836).
%Y A340856 A112798 lists the prime indices of each positive integer.
%Y A340856 A200750 counts partitions with length coprime to maximum (A340608).
%Y A340856 A257541 gives the rank of the partition with Heinz number n.
%Y A340856 A340830 counts strict partitions whose parts are multiples of the length.
%Y A340856 Cf. A039900, A047993 (A106529), A064174, A143773 (A316428), A326837, A326849 (A326848), A340599, A340691.
%K A340856 nonn
%O A340856 1,1
%A A340856 _Gus Wiseman_, Feb 05 2021