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A338557 Products of three distinct prime numbers of even index. 4
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

Table of n, a(n) for n=1..44.

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.

Cf. A000217, A001221, A001222, A037144, A056239, A112798, A337605.

Sequence in context: A043821 A217004 A256638 * A306812 A157374 A043467

Adjacent sequences:  A338554 A338555 A338556 * A338558 A338559 A338560

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.)