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 A325043 Heinz numbers of integer partitions, with at least three parts, whose product of parts is one fewer than their sum. 0
 18, 60, 168, 216, 400, 528, 1248, 2240, 2880, 3264, 7296, 14080, 17664, 25088, 32256, 41472, 44544, 66560, 95232, 153600, 227328, 315392, 348160, 405504, 503808, 1056768, 1556480, 2310144, 2981888, 3833856, 5210112, 6881280, 7536640, 7929856, 8847360, 11599872 (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 with at least three prime factors (counted with multiplicity) whose product of prime indices (A003963) is one fewer than their sum of prime indices (A056239). LINKS Table of n, a(n) for n=1..36. FORMULA a(n) = 2 * A301988(n). EXAMPLE The sequence of terms together with their prime indices begins: 18: {1,2,2} 60: {1,1,2,3} 168: {1,1,1,2,4} 216: {1,1,1,2,2,2} 400: {1,1,1,1,3,3} 528: {1,1,1,1,2,5} 1248: {1,1,1,1,1,2,6} 2240: {1,1,1,1,1,1,3,4} 2880: {1,1,1,1,1,1,2,2,3} 3264: {1,1,1,1,1,1,2,7} 7296: {1,1,1,1,1,1,1,2,8} 14080: {1,1,1,1,1,1,1,1,3,5} 17664: {1,1,1,1,1,1,1,1,2,9} 25088: {1,1,1,1,1,1,1,1,1,4,4} 32256: {1,1,1,1,1,1,1,1,1,2,2,4} 41472: {1,1,1,1,1,1,1,1,1,2,2,2,2} 44544: {1,1,1,1,1,1,1,1,1,2,10} 66560: {1,1,1,1,1,1,1,1,1,1,3,6} 95232: {1,1,1,1,1,1,1,1,1,1,2,11} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[10000], And[PrimeOmega[#]>2, Times@@primeMS[#]==Total[primeMS[#]]-1]&] CROSSREFS Cf. A000720, A003963, A056239, A112798, A178503, A175508, A301987, A319000. Cf. A325032, A325033, A325036, A325037, A325038, A325041, A325042, A325044. Sequence in context: A218617 A105521 A154563 * A338536 A090073 A327089 Adjacent sequences: A325040 A325041 A325042 * A325044 A325045 A325046 KEYWORD nonn AUTHOR Gus Wiseman, Mar 25 2019 EXTENSIONS More terms from Jinyuan Wang, Jun 27 2020 STATUS approved

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Last modified February 21 15:08 EST 2024. Contains 370236 sequences. (Running on oeis4.)