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A340932 Numbers whose least prime index is odd. Heinz numbers of integer partitions whose last part is odd.

%I A340932 #14 Feb 14 2021 01:40:19
%S A340932 2,4,5,6,8,10,11,12,14,16,17,18,20,22,23,24,25,26,28,30,31,32,34,35,
%T A340932 36,38,40,41,42,44,46,47,48,50,52,54,55,56,58,59,60,62,64,65,66,67,68,
%U A340932 70,72,73,74,76,78,80,82,83,84,85,86,88,90,92,94,95,96,97
%N A340932 Numbers whose least prime index is odd. Heinz numbers of integer partitions whose last part is odd.
%C A340932 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. 1 has no prime indices so is not included.
%F A340932 A055396(a(n)) belongs to A005408.
%F A340932 Closed under multiplication.
%e A340932 The sequence of terms together with their prime indices begins:
%e A340932       2: {1}           24: {1,1,1,2}       46: {1,9}
%e A340932       4: {1,1}         25: {3,3}           47: {15}
%e A340932       5: {3}           26: {1,6}           48: {1,1,1,1,2}
%e A340932       6: {1,2}         28: {1,1,4}         50: {1,3,3}
%e A340932       8: {1,1,1}       30: {1,2,3}         52: {1,1,6}
%e A340932      10: {1,3}         31: {11}            54: {1,2,2,2}
%e A340932      11: {5}           32: {1,1,1,1,1}     55: {3,5}
%e A340932      12: {1,1,2}       34: {1,7}           56: {1,1,1,4}
%e A340932      14: {1,4}         35: {3,4}           58: {1,10}
%e A340932      16: {1,1,1,1}     36: {1,1,2,2}       59: {17}
%e A340932      17: {7}           38: {1,8}           60: {1,1,2,3}
%e A340932      18: {1,2,2}       40: {1,1,1,3}       62: {1,11}
%e A340932      20: {1,1,3}       41: {13}            64: {1,1,1,1,1,1}
%e A340932      22: {1,5}         42: {1,2,4}         65: {3,6}
%e A340932      23: {9}           44: {1,1,5}         66: {1,2,5}
%t A340932 Select[Range[100],OddQ[PrimePi[FactorInteger[#][[1,1]]]]&]
%Y A340932 These partitions are counted by A026804.
%Y A340932 The case where all prime indices are odd is A066208.
%Y A340932 Looking at greatest prime index instead of least gives A244991.
%Y A340932 Every term x is a product of A257991(x) elements of A341446.
%Y A340932 The complement is {1} \/ A340933, counted by A026805.
%Y A340932 A001222 counts prime factors.
%Y A340932 A005408 lists odd numbers.
%Y A340932 A027193 counts odd-length partitions, ranked by A026424.
%Y A340932 A031368 lists odd-indexed primes.
%Y A340932 A055396 selects least prime index.
%Y A340932 A056239 adds up prime indices.
%Y A340932 A058695 counts partitions of odd numbers, ranked by A300063.
%Y A340932 A061395 selects greatest prime index.
%Y A340932 A112798 lists the prime indices of each positive integer.
%Y A340932 Cf. A006141, A160786, A300272, A340604, A340854, A340855.
%K A340932 nonn
%O A340932 1,1
%A A340932 _Gus Wiseman_, Feb 12 2021