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 A327784 Heinz numbers of integer partitions whose LCM is greater than their sum. 4
 1, 15, 33, 35, 51, 55, 66, 69, 70, 77, 85, 91, 93, 95, 99, 102, 105, 110, 119, 123, 132, 138, 140, 141, 143, 145, 153, 154, 155, 161, 165, 170, 175, 177, 182, 186, 187, 190, 201, 203, 204, 205, 207, 209, 210, 215, 217, 219, 220, 221, 231, 238, 245, 246, 247, 249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS FORMULA A290103(a(k)) > A056239(a(k)). EXAMPLE The sequence of terms together with their prime indices begins:     1: {}    15: {2,3}    33: {2,5}    35: {3,4}    51: {2,7}    55: {3,5}    66: {1,2,5}    69: {2,9}    70: {1,3,4}    77: {4,5}    85: {3,7}    91: {4,6}    93: {2,11}    95: {3,8}    99: {2,2,5}   102: {1,2,7}   105: {2,3,4}   110: {1,3,5}   119: {4,7}   123: {2,13}   132: {1,1,2,5} MAPLE q:= n-> (l-> is(ilcm(l[])>add(j, j=l)))(map(i->     numtheory[pi](i[1])\$i[2], ifactors(n)[2])): select(q, [\$1..250])[];  # Alois P. Heinz, Sep 27 2019 MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[2, 100], LCM@@primeMS[#]>Total[primeMS[#]]&] CROSSREFS The enumeration of these partitions by sum is A327779. Heinz numbers of partitions whose LCM is twice their sum are A327775. Heinz numbers of partitions whose LCM is less than their sum are A327776. Heinz numbers of partitions whose LCM is a multiple their sum are A327783. Cf. A056239, A074761, A112798, A290103, A316413, A326841, A327781. Sequence in context: A154369 A243592 A089966 * A339562 A338468 A337984 Adjacent sequences:  A327781 A327782 A327783 * A327785 A327786 A327787 KEYWORD nonn AUTHOR Gus Wiseman, Sep 25 2019 STATUS approved

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)