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A338469 Products of three odd prime numbers of odd index. 2
125, 275, 425, 575, 605, 775, 935, 1025, 1175, 1265, 1331, 1445, 1475, 1675, 1705, 1825, 1955, 2057, 2075, 2255, 2425, 2575, 2585, 2635, 2645, 2725, 2783, 3175, 3179, 3245, 3425, 3485, 3565, 3685, 3725, 3751, 3925, 3995, 4015, 4175, 4301, 4475, 4565, 4715 (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 and > 1. These partitions are counted by A001399.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The sequence of terms together with their prime indices begins:

     125: {3,3,3}     1825: {3,3,21}    3425: {3,3,33}

     275: {3,3,5}     1955: {3,7,9}     3485: {3,7,13}

     425: {3,3,7}     2057: {5,5,7}     3565: {3,9,11}

     575: {3,3,9}     2075: {3,3,23}    3685: {3,5,19}

     605: {3,5,5}     2255: {3,5,13}    3725: {3,3,35}

     775: {3,3,11}    2425: {3,3,25}    3751: {5,5,11}

     935: {3,5,7}     2575: {3,3,27}    3925: {3,3,37}

    1025: {3,3,13}    2585: {3,5,15}    3995: {3,7,15}

    1175: {3,3,15}    2635: {3,7,11}    4015: {3,5,21}

    1265: {3,5,9}     2645: {3,9,9}     4175: {3,3,39}

    1331: {5,5,5}     2725: {3,3,29}    4301: {5,7,9}

    1445: {3,7,7}     2783: {5,5,9}     4475: {3,3,41}

    1475: {3,3,17}    3175: {3,3,31}    4565: {3,5,23}

    1675: {3,3,19}    3179: {5,7,7}     4715: {3,9,13}

    1705: {3,5,11}    3245: {3,5,17}    4775: {3,3,43}

MAPLE

N:= 10000: # for terms <= N

P0:= [seq(ithprime(i), i=3..numtheory:-pi(floor(N/25)), 2)]:

sort(select(`<=`, [seq(seq(seq(P0[i]*P0[j]*P0[k], k=1..j), j=1..i), i=1..nops(P0))], N)); # Robert Israel, Nov 12 2020

MATHEMATICA

Select[Range[1, 1000, 2], PrimeOmega[#]==3&&OddQ[Times@@PrimePi/@First/@FactorInteger[#]]&]

PROG

(PARI) isok(m) = my(f=factor(m)); (m%2) && (bigomega(f)==3) && (#select(x->!(x%2), apply(primepi, f[, 1]~)) == 0); \\ Michel Marcus, Nov 10 2020

CROSSREFS

A046316 allows all primes (strict: A046389).

A338471 allows all odd primes (strict: A307534).

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)).

A005408 lists odds (strict: A056911).

A008284 counts partitions by sum and length.

A014311 is a ranking of 3-part compositions (strict: A337453).

A014612 lists Heinz numbers of 3-part partitions (strict: A007304).

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

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

A066208 lists numbers with all odd prime indices (strict: A258116).

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

A285508 lists Heinz numbers of non-strict 3-part partitions.

Cf. A001221, A001222, A002620, A005117, A037144, A056239, A112798.

Sequence in context: A260604 A023079 A172460 * A253226 A223182 A256362

Adjacent sequences:  A338466 A338467 A338468 * A338470 A338471 A338472

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 08 2020

STATUS

approved

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Last modified November 28 09:55 EST 2021. Contains 349401 sequences. (Running on oeis4.)