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A324517 Numbers > 1 where the maximum prime index equals the number of prime factors minus the number of distinct prime factors. 11
4, 24, 27, 36, 54, 80, 200, 224, 240, 360, 405, 500, 540, 600, 625, 672, 675, 704, 784, 810, 900, 1008, 1120, 1125, 1250, 1350, 1500, 1512, 1664, 1701, 1875, 2112, 2250, 2268, 2352, 2744, 2800, 3168, 3360, 3402, 3520, 3528, 3750, 3872, 3920, 3969, 4352, 4752 (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.

Also Heinz numbers of the integer partitions enumerated by A324518. 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..48.

FORMULA

A061395(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).

EXAMPLE

The sequence of terms together with their prime indices begins:

    4: {1,1}

   24: {1,1,1,2}

   27: {2,2,2}

   36: {1,1,2,2}

   54: {1,2,2,2}

   80: {1,1,1,1,3}

  200: {1,1,1,3,3}

  224: {1,1,1,1,1,4}

  240: {1,1,1,1,2,3}

  360: {1,1,1,2,2,3}

  405: {2,2,2,2,3}

  500: {1,1,3,3,3}

  540: {1,1,2,2,2,3}

  600: {1,1,1,2,3,3}

  625: {3,3,3,3}

  672: {1,1,1,1,1,2,4}

  675: {2,2,2,3,3}

  704: {1,1,1,1,1,1,5}

  784: {1,1,1,1,4,4}

  810: {1,2,2,2,2,3}

  900: {1,1,2,2,3,3}

MATHEMATICA

Select[Range[2, 1000], With[{f=FactorInteger[#]}, PrimePi[f[[-1, 1]]]==Total[Last/@f]-Length[f]]&]

CROSSREFS

Cf. A001221, A001222, A046660, A056239, A061395, A112798, A243055, A256617.

Cf. A324515, A324518, A324519, A324521, A324522, A324560, A324562.

Sequence in context: A222595 A103225 A303333 * A137980 A144137 A238222

Adjacent sequences:  A324514 A324515 A324516 * A324518 A324519 A324520

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 06 2019

STATUS

approved

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Last modified April 21 15:55 EDT 2021. Contains 343156 sequences. (Running on oeis4.)