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A338556 Products of three prime numbers of even index. 5
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

Table of n, a(n) for n=1..48.

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.

Cf. A000217, A001221, A001222, A037144, A056239, A112798, A337599, A337600.

Subsequence of A332820.

Sequence in context: A128530 A044129 A044510 * A304563 A304557 A088248

Adjacent sequences:  A338553 A338554 A338555 * A338557 A338558 A338559

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 08 2020

STATUS

approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)