The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325044 Heinz numbers of integer partitions whose sum of parts is greater than or equal to their product. 25
 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 60, 61, 62, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 82, 83, 84, 86, 88, 89, 92, 94, 96, 97, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose product of prime indices (A003963) is less than or equal to their sum of prime indices (A056239). The enumeration of these partitions by sum is given by A096276. LINKS Table of n, a(n) for n=1..67. FORMULA A003963(a(n)) <= A056239(a(n)). a(n) = A325038(n)/2. Union of A301987 and A325038. EXAMPLE The sequence of terms together with their prime indices begins: 2: {1} 3: {2} 4: {1,1} 5: {3} 6: {1,2} 7: {4} 8: {1,1,1} 9: {2,2} 10: {1,3} 11: {5} 12: {1,1,2} 13: {6} 14: {1,4} 16: {1,1,1,1} 17: {7} 18: {1,2,2} 19: {8} 20: {1,1,3} 22: {1,5} 23: {9} 24: {1,1,1,2} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], Times@@primeMS[#]<=Plus@@primeMS[#]&] CROSSREFS Cf. A000720, A003963, A056239, A112798, A178503, A175508, A301987, A319000. Cf. A325032, A325033, A325036, A325037, A325038, A325041, A325042. Sequence in context: A070776 A320230 A076564 * A343822 A303550 A164563 Adjacent sequences: A325041 A325042 A325043 * A325045 A325046 A325047 KEYWORD nonn AUTHOR Gus Wiseman, Mar 25 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 25 21:07 EST 2024. Contains 370333 sequences. (Running on oeis4.)