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A338471 Products of three prime numbers of odd index. 5
8, 20, 44, 50, 68, 92, 110, 124, 125, 164, 170, 188, 230, 236, 242, 268, 275, 292, 310, 332, 374, 388, 410, 412, 425, 436, 470, 506, 508, 548, 575, 578, 590, 596, 605, 628, 668, 670, 682, 716, 730, 764, 775, 782, 788, 830, 844, 902, 908, 932, 935, 964, 970 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also Heinz numbers of integer partitions with 3 parts, all of which are odd. These partitions are counted by A001399.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

The sequence of terms together with their prime indices begins:

       8: {1,1,1}      268: {1,1,19}     575: {3,3,9}

      20: {1,1,3}      275: {3,3,5}      578: {1,7,7}

      44: {1,1,5}      292: {1,1,21}     590: {1,3,17}

      50: {1,3,3}      310: {1,3,11}     596: {1,1,35}

      68: {1,1,7}      332: {1,1,23}     605: {3,5,5}

      92: {1,1,9}      374: {1,5,7}      628: {1,1,37}

     110: {1,3,5}      388: {1,1,25}     668: {1,1,39}

     124: {1,1,11}     410: {1,3,13}     670: {1,3,19}

     125: {3,3,3}      412: {1,1,27}     682: {1,5,11}

     164: {1,1,13}     425: {3,3,7}      716: {1,1,41}

     170: {1,3,7}      436: {1,1,29}     730: {1,3,21}

     188: {1,1,15}     470: {1,3,15}     764: {1,1,43}

     230: {1,3,9}      506: {1,5,9}      775: {3,3,11}

     236: {1,1,17}     508: {1,1,31}     782: {1,7,9}

     242: {1,5,5}      548: {1,1,33}     788: {1,1,45}

MATHEMATICA

Select[Range[100], PrimeOmega[#]==3&&OddQ[Times@@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

A066208 allows products of any length (strict: A258116).

A307534 is the squarefree case.

A338469 is the restriction to odds.

A338556 is the version for evens (strict: A338557).

A000009 counts partitions into odd parts (strict: A000700).

A001399(n-3) counts 3-part partitions (strict: A001399(n-6)).

A008284 counts partitions by sum and length.

A014311 is a ranking of ordered triples (strict: A337453).

A014612 lists Heinz numbers of all triples (strict: A007304).

A023023 counts 3-part relatively prime partitions (strict: A101271).

A023023 counts 3-part relatively prime partitions (strict: A078374).

A046316 lists products of exactly three odd primes (strict: A046389).

A066207 lists numbers with all even prime indices (strict: A258117).

A075818 lists even Heinz numbers of 3-part partitions (strict: A075819).

A285508 lists Heinz numbers of non-strict triples.

A307719 counts 3-part pairwise coprime partitions (strict: A220377).

Cf. A000217, A001221, A001222, A005117, A037144, A056239, A112798.

Subsequence of A332820.

Sequence in context: A308904 A192753 A121307 * A086169 A273241 A273295

Adjacent sequences:  A338467 A338468 A338469 * A338472 A338473 A338474

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 08 2020

STATUS

approved

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Last modified April 10 06:54 EDT 2021. Contains 342843 sequences. (Running on oeis4.)