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A324929
Numbers whose product of prime indices is even.
18
3, 6, 7, 9, 12, 13, 14, 15, 18, 19, 21, 24, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 42, 43, 45, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 61, 63, 65, 66, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 84, 86, 87, 89, 90, 91, 93, 95, 96, 98, 99, 101, 102, 104
OFFSET
1,1
COMMENTS
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, with product A003963(n).
Also Heinz numbers of integer partitions whose product of parts is even (counted by A047967), where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
6: {1,2}
7: {4}
9: {2,2}
12: {1,1,2}
13: {6}
14: {1,4}
15: {2,3}
18: {1,2,2}
19: {8}
21: {2,4}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
29: {10}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
MATHEMATICA
Select[Range[100], EvenQ[Times@@PrimePi/@If[#==1, {}, FactorInteger[#]][[All, 1]]]&]
PROG
(PARI) isok(n) = my(f=factor(n)[, 1]); !(prod(k=1, #f, primepi(f[k])) % 2); \\ Michel Marcus, Mar 22 2019
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved