A326836 - OEIS

A326836

Heinz numbers of integer partitions whose maximum part divides their sum.

2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 36, 37, 40, 41, 43, 47, 48, 49, 53, 59, 61, 63, 64, 67, 70, 71, 73, 79, 81, 83, 84, 89, 97, 101, 103, 107, 108, 109, 112, 113, 121, 125, 127, 128, 131, 135, 137, 139, 144, 149, 150, 151

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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 maximum prime index divides their sum of prime indices.

The enumeration of these partitions by sum is given by A067538.

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

The sequence of terms together with their prime indices begins:

2: {1}

3: {2}

4: {1,1}

5: {3}

7: {4}

8: {1,1,1}

9: {2,2}

11: {5}

12: {1,1,2}

13: {6}

16: {1,1,1,1}

17: {7}

19: {8}

23: {9}

25: {3,3}

27: {2,2,2}

29: {10}

30: {1,2,3}

31: {11}

32: {1,1,1,1,1}

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[200], Divisible[Total[primeMS[#]], Max[primeMS[#]]]&]

CROSSREFS

Cf. A018818, A047993, A056239, A061395, A067538, A112798, A316413.

Cf. A326837, A326838, A326839/A326840, A326841, A326843, A326850.

Sequence in context: A085233 A357861 A133813 * A326841 A274222 A300273

Adjacent sequences: A326833 A326834 A326835 * A326837 A326838 A326839

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 26 2019

STATUS

approved