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A325240 Numbers whose minimum prime exponent is 2. 3
4, 9, 25, 36, 49, 72, 100, 108, 121, 144, 169, 196, 200, 225, 288, 289, 324, 361, 392, 400, 441, 484, 500, 529, 576, 675, 676, 784, 800, 841, 900, 961, 968, 972, 1089, 1125, 1152, 1156, 1225, 1323, 1352, 1369, 1372, 1444, 1521, 1568, 1600, 1681, 1764, 1800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or barely powerful numbers, a subset of powerful numbers A001694.

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 minimum multiplicity is 2 (counted by A244515).

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

The sequence of terms together with their prime indices begins:

    4: {1,1}

    9: {2,2}

   25: {3,3}

   36: {1,1,2,2}

   49: {4,4}

   72: {1,1,1,2,2}

  100: {1,1,3,3}

  108: {1,1,2,2,2}

  121: {5,5}

  144: {1,1,1,1,2,2}

  169: {6,6}

  196: {1,1,4,4}

  200: {1,1,1,3,3}

  225: {2,2,3,3}

  288: {1,1,1,1,1,2,2}

  289: {7,7}

  324: {1,1,2,2,2,2}

  361: {8,8}

  392: {1,1,1,4,4}

  400: {1,1,1,1,3,3}

MATHEMATICA

Select[Range[1000], Min@@FactorInteger[#][[All, 2]]==2&]

CROSSREFS

Positions of 2's in A051904.

Maximum instead of minimum gives A067259.

Cf. A001221, A001222, A001358, A001694, A007774, A051903, A052485, A118914, A244515, A325241.

Sequence in context: A182120 A099998 A030140 * A153158 A111245 A062503

Adjacent sequences:  A325237 A325238 A325239 * A325241 A325242 A325243

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 15 2019

STATUS

approved

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)