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A338556 Products of three prime numbers of even index. 6
27, 63, 117, 147, 171, 261, 273, 333, 343, 387, 399, 477, 507, 549, 609, 637, 639, 711, 741, 777, 801, 903, 909, 931, 963, 1017, 1083, 1113, 1131, 1179, 1183, 1251, 1281, 1359, 1421, 1443, 1467, 1491, 1557, 1629, 1653, 1659, 1677, 1729, 1737, 1791, 1813, 1869 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are odd.
Also Heinz numbers of 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:
27: {2,2,2} 637: {4,4,6} 1183: {4,6,6}
63: {2,2,4} 639: {2,2,20} 1251: {2,2,34}
117: {2,2,6} 711: {2,2,22} 1281: {2,4,18}
147: {2,4,4} 741: {2,6,8} 1359: {2,2,36}
171: {2,2,8} 777: {2,4,12} 1421: {4,4,10}
261: {2,2,10} 801: {2,2,24} 1443: {2,6,12}
273: {2,4,6} 903: {2,4,14} 1467: {2,2,38}
333: {2,2,12} 909: {2,2,26} 1491: {2,4,20}
343: {4,4,4} 931: {4,4,8} 1557: {2,2,40}
387: {2,2,14} 963: {2,2,28} 1629: {2,2,42}
399: {2,4,8} 1017: {2,2,30} 1653: {2,8,10}
477: {2,2,16} 1083: {2,8,8} 1659: {2,4,22}
507: {2,6,6} 1113: {2,4,16} 1677: {2,6,14}
549: {2,2,18} 1131: {2,6,10} 1729: {4,6,8}
609: {2,4,10} 1179: {2,2,32} 1737: {2,2,44}
MATHEMATICA
Select[Range[1000], PrimeOmega[#]==3&&OddQ[Times@@(1+PrimePi/@First/@FactorInteger[#])]&]
PROG
(PARI) isok(m) = my(f=factor(m)); (bigomega(f)==3) && (#select(x->(x%2), apply(primepi, f[, 1]~)) == 0); \\ Michel Marcus, Nov 10 2020
CROSSREFS
A014612 allows all prime indices (not just even) (strict: A007304).
A066207 allows products of any length (strict: A258117).
A338471 is the version for odds instead of evens (strict: A307534).
A338557 is the strict case.
A014311 is a ranking of ordered triples (strict: A337453).
A001399(n-3) counts 3-part partitions (strict: A001399(n-6)).
A005117 lists squarefree numbers, with even case A039956.
A008284 counts partitions by sum and length (strict: A008289).
A023023 counts 3-part relatively prime partitions (strict: A101271).
A046316 lists products of exactly three odd primes (strict: A046389).
A066208 lists numbers with all odd prime indices (strict: A258116).
A075818 lists even Heinz numbers of 3-part partitions (strict: A075819).
A307719 counts 3-part pairwise coprime partitions (strict: A220377).
A285508 lists Heinz numbers of non-strict triples.
Subsequence of A332820.
Sequence in context: A373763 A044129 A044510 * A304563 A304557 A372976
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 08 2020
STATUS
approved

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Last modified August 18 15:26 EDT 2024. Contains 375269 sequences. (Running on oeis4.)