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A338557 Products of three distinct prime numbers of even index. 5
273, 399, 609, 741, 777, 903, 1113, 1131, 1281, 1443, 1491, 1653, 1659, 1677, 1729, 1869, 2067, 2109, 2121, 2247, 2373, 2379, 2451, 2639, 2751, 2769, 2919, 3021, 3081, 3171, 3219, 3367, 3423, 3471, 3477, 3633, 3741, 3801, 3857, 3913, 3939, 4047, 4053, 4173 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are odd.
Also sphenic numbers (A007304) with all even prime indices (A031215).
Also Heinz numbers of strict integer partitions with 3 parts, all of which are even. These partitions are counted by A001399.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
273: {2,4,6} 1869: {2,4,24} 3219: {2,10,12}
399: {2,4,8} 2067: {2,6,16} 3367: {4,6,12}
609: {2,4,10} 2109: {2,8,12} 3423: {2,4,38}
741: {2,6,8} 2121: {2,4,26} 3471: {2,6,24}
777: {2,4,12} 2247: {2,4,28} 3477: {2,8,18}
903: {2,4,14} 2373: {2,4,30} 3633: {2,4,40}
1113: {2,4,16} 2379: {2,6,18} 3741: {2,10,14}
1131: {2,6,10} 2451: {2,8,14} 3801: {2,4,42}
1281: {2,4,18} 2639: {4,6,10} 3857: {4,8,10}
1443: {2,6,12} 2751: {2,4,32} 3913: {4,6,14}
1491: {2,4,20} 2769: {2,6,20} 3939: {2,6,26}
1653: {2,8,10} 2919: {2,4,34} 4047: {2,8,20}
1659: {2,4,22} 3021: {2,8,16} 4053: {2,4,44}
1677: {2,6,14} 3081: {2,6,22} 4173: {2,6,28}
1729: {4,6,8} 3171: {2,4,36} 4179: {2,4,46}
MATHEMATICA
Select[Range[1000], SquareFreeQ[#]&&PrimeOmega[#]==3&&OddQ[Times@@(1+PrimePi/@First/@FactorInteger[#])]&]
PROG
(PARI) isok(m) = my(f=factor(m)); (bigomega(f)==3) && (omega(f)==3) && (#select(x->(x%2), apply(primepi, f[, 1]~)) == 0); \\ Michel Marcus, Nov 10 2020
CROSSREFS
For the following, NNS means "not necessarily strict".
A007304 allows all prime indices (not just even) (NNS: A014612).
A046389 allows all odd primes (NNS: A046316).
A258117 allows products of any length (NNS: A066207).
A307534 is the version for odds instead of evens (NNS: A338471).
A337453 is a different ranking of ordered triples (NNS: A014311).
A338556 is the NNS version.
A001399(n-6) counts strict 3-part partitions (NNS: A001399(n-3)).
A005117 lists squarefree numbers, with even case A039956.
A078374 counts 3-part relatively prime strict partitions (NNS: A023023).
A075819 lists even Heinz numbers of strict triples (NNS: A075818).
A220377 counts 3-part pairwise coprime strict partitions (NNS: A307719).
A258116 lists squarefree numbers with all odd prime indices (NNS: A066208).
A285508 lists Heinz numbers of non-strict triples.
Sequence in context: A043821 A217004 A256638 * A347882 A347888 A306812
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 08 2020
STATUS
approved

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Last modified February 25 17:53 EST 2024. Contains 370332 sequences. (Running on oeis4.)