The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A327415 Representation of integers by the product of prime partitions. 1
 0, 1, 2, 3, 4, 5, 9, 7, 15, 14, 21, 11, 35, 13, 33, 26, 39, 17, 65, 19, 51, 38, 57, 23, 95, 46, 69, 92, 115, 29, 161, 31, 87, 62, 93, 124, 155, 37, 217, 74, 111, 41, 185, 43, 123, 86, 129, 47, 215, 94, 141, 188, 235, 53, 329, 106, 159, 212, 265, 59, 371, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A partition is prime if all parts are primes. A partition of an odd integer is minimal if it has at most one odd part and is shorter than any other such partition. A partition of an even integer n > 2 is minimal if it has at most two parts, one of which is the greatest prime less than n - 1. The terms of the sequence are the products of these partitions. For n in {0, 1, 2} a(n) = n by convention. LINKS Eric Weisstein's World of Mathematics, Prime Partition EXAMPLE n   a(n)  partition 2     2    3     3    4     4   [2, 2] 5     5    6     9   [3, 3] 7     7    8    15   [5, 3] 9    14   [7, 2] 10   21   [7, 3] 11   11    12   35   [7, 5] 13   13    14   33   [11, 3] 15   26   [13, 2] 16   39   [13, 3] 17   17    18   65   [13, 5] 19   19    20   51   [17, 3] MAPLE a := proc(n) local r, p;     if n <= 2 then return n fi;     if n::odd then         if isprime(n) then return n fi;         r := prevprime(n);         p := [seq(2, i=1..(n + 1 - r)/2), r]     else         r := prevprime(n - 1);         p := [n - r, r]     fi;     return mul(k, k in p) end: seq(a(n), n = 0..61); PROG (SageMath) def a(n):     if n <= 2: return n     if n % 2 == 1:         if is_prime(n): return n         r = previous_prime(n)         p = [r] + *((n + 1 - r)//2)     else:         r = previous_prime(n - 1)         p = [r, n - r]     return mul(p) print([a(n) for n in range(40)]) CROSSREFS Sequence in context: A222257 A327456 A238535 * A072501 A092975 A164340 Adjacent sequences:  A327412 A327413 A327414 * A327416 A327417 A327418 KEYWORD nonn AUTHOR Peter Luschny, Sep 08 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 30 12:08 EDT 2021. Contains 346359 sequences. (Running on oeis4.)