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 A326149 Numbers whose product of prime indices is divisible by their sum of prime indices. 17
 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 43, 47, 49, 53, 59, 61, 63, 65, 67, 71, 73, 79, 81, 83, 84, 89, 97, 101, 103, 107, 108, 109, 113, 125, 127, 131, 137, 139, 149, 150, 151, 154, 157, 163, 165, 167, 169, 173, 179, 181, 190, 191, 193, 197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose product of parts is divisible by their sum of parts. The enumeration of these partitions by sum is given by A057568. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     2: {1}     3: {2}     5: {3}     7: {4}     9: {2,2}    11: {5}    13: {6}    17: {7}    19: {8}    23: {9}    29: {10}    30: {1,2,3}    31: {11}    37: {12}    41: {13}    43: {14}    47: {15}    49: {4,4}    53: {16}    59: {17} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[2, 100], Divisible[Times@@primeMS[#], Plus@@primeMS[#]]&] CROSSREFS Satisfies A056239(a(n))|A003963(a(n)). The nonprime case is A326150, with squarefree case A326158. Cf. A000720, A001222, A057567, A057568, A112798, A301987. Cf. A325037, A325042, A325044, A326151, A326153/A326154, A326155, A326156. Sequence in context: A325623 A136327 A095415 * A301987 A316857 A318589 Adjacent sequences:  A326146 A326147 A326148 * A326150 A326151 A326152 KEYWORD nonn AUTHOR Gus Wiseman, Jun 09 2019 STATUS approved

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Last modified March 29 20:20 EDT 2020. Contains 333117 sequences. (Running on oeis4.)