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 A087942 Number of partitions of n into as many primes as n has prime factors. 1
 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 7, 1, 3, 7, 3, 1, 2, 1, 11, 1, 4, 0, 15, 1, 2, 1, 21, 1, 3, 1, 4, 12, 4, 1, 26, 1, 5, 0, 4, 1, 33, 1, 38, 0, 4, 1, 41, 1, 3, 19, 137, 0, 5, 1, 6, 1, 2, 1, 61, 1, 5, 22, 5, 0, 5, 1, 67, 24, 5, 1, 81, 1, 5, 0, 96, 1, 93, 1, 9, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Conjecture, for m>1: a(m)=0 iff n is an odd semiprime such that m-2 is not prime, i.e. m=A089268(k) for some k. - Reinhard Zumkeller, Oct 28 2003 LINKS Table of n, a(n) for n=1..93. Eric Weisstein's World of Mathematics, Prime Partition. Index entries for sequences related to Goldbach conjecture EXAMPLE n=20 = 2*2*5 = 13+5+2 = 11+7+2, all other partitions into 3 primes have fewer than or more than 3 parts, therefore a(20)=2. MATHEMATICA Table[Count[IntegerPartitions[n, {PrimeOmega[n]}], _?(AllTrue[#, PrimeQ]&)], {n, 100}] (* Harvey P. Dale, Jul 26 2023 *) CROSSREFS Cf. A001222, A000607, A051034, A004526. Sequence in context: A363228 A235726 A060938 * A359237 A327925 A320012 Adjacent sequences: A087939 A087940 A087941 * A087943 A087944 A087945 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 27 2003 STATUS approved

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Last modified September 30 02:50 EDT 2023. Contains 365781 sequences. (Running on oeis4.)