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A307534 Heinz numbers of strict integer partitions with 3 parts, all of which are odd. 9
110, 170, 230, 310, 374, 410, 470, 506, 590, 670, 682, 730, 782, 830, 902, 935, 970, 1030, 1034, 1054, 1090, 1265, 1270, 1298, 1370, 1394, 1426, 1474, 1490, 1570, 1598, 1606, 1670, 1705, 1790, 1826, 1886, 1910, 1955, 1970, 2006, 2110, 2134, 2162, 2255, 2266 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The enumeration of these partitions by sum is given by A001399.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..46.

EXAMPLE

The sequence of terms together with their prime indices begins:

   110: {1,3,5}

   170: {1,3,7}

   230: {1,3,9}

   310: {1,3,11}

   374: {1,5,7}

   410: {1,3,13}

   470: {1,3,15}

   506: {1,5,9}

   590: {1,3,17}

   670: {1,3,19}

   682: {1,5,11}

   730: {1,3,21}

   782: {1,7,9}

   830: {1,3,23}

   902: {1,5,13}

   935: {3,5,7}

   970: {1,3,25}

  1030: {1,3,27}

  1034: {1,5,15}

  1054: {1,7,11}

MATHEMATICA

Select[Range[1000], SquareFreeQ[#]&&PrimeNu[#]==3&&OddQ[Times@@PrimePi/@First/@FactorInteger[#]]&]

CROSSREFS

Cf. A001221, A001222, A001399, A005117, A007304, A014612, A037144, A051037, A056239, A080193, A080257, A112798, A143207, A304636.

Sequence in context: A039447 A095611 A335272 * A200070 A324210 A146081

Adjacent sequences:  A307531 A307532 A307533 * A307535 A307536 A307537

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 13 2019

STATUS

approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)