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A324515 Numbers > 1 where the maximum prime index minus the minimum prime index equals the number of prime factors minus the number of distinct prime factors. 6
2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 23, 29, 31, 37, 40, 41, 43, 45, 47, 53, 59, 61, 67, 71, 73, 75, 79, 83, 89, 97, 100, 101, 103, 107, 109, 112, 113, 120, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 175, 179, 180, 181, 189, 191, 193, 197, 199, 211, 223 (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 A324516. 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..59.

FORMULA

A243055(a(n)) = A061395(a(n)) - A055396(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).

EXAMPLE

The sequence of terms together with their prime indices begins:

   2: {1}

   3: {2}

   5: {3}

   7: {4}

  11: {5}

  12: {1,1,2}

  13: {6}

  17: {7}

  18: {1,2,2}

  19: {8}

  23: {9}

  29: {10}

  31: {11}

  37: {12}

  40: {1,1,1,3}

  41: {13}

  43: {14}

  45: {2,2,3}

MATHEMATICA

Select[Range[2, 100], With[{f=FactorInteger[#]}, PrimePi[f[[-1, 1]]]-PrimePi[f[[1, 1]]]==Total[Last/@f]-Length[f]]&]

CROSSREFS

Cf. A001221, A001222, A006141, A046660, A047993, A055396, A056239, A061395, A106529, A112798, A243055.

Cf. A324516, A324517, A324519, A324521, A324522, A324560, A324562.

Sequence in context: A212166 A293511 A325337 * A212127 A307895 A028835

Adjacent sequences:  A324512 A324513 A324514 * A324516 A324517 A324518

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 06 2019

STATUS

approved

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)