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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 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.)