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A327685 Nonprime numbers whose prime indices have a common divisor > 1. 3
9, 21, 25, 27, 39, 49, 57, 63, 65, 81, 87, 91, 111, 115, 117, 121, 125, 129, 133, 147, 159, 169, 171, 183, 185, 189, 203, 213, 235, 237, 243, 247, 259, 261, 267, 273, 289, 299, 301, 303, 305, 319, 321, 325, 333, 339, 343, 351, 361, 365, 371, 377, 387, 393, 399 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First differs from A322336 in lacking 2535 = prime(2)*prime(3)*prime(6)^2.

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. Heinz numbers of integer partitions with a common divisor > 1 are A318978, and the enumeration of these partitions by sum is A108572.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Complement of A000040 in A318978.

EXAMPLE

The sequence of terms together with their prime indices begins:

    9: {2,2}

   21: {2,4}

   25: {3,3}

   27: {2,2,2}

   39: {2,6}

   49: {4,4}

   57: {2,8}

   63: {2,2,4}

   65: {3,6}

   81: {2,2,2,2}

   87: {2,10}

   91: {4,6}

  111: {2,12}

  115: {3,9}

  117: {2,2,6}

  121: {5,5}

  125: {3,3,3}

  129: {2,14}

  133: {4,8}

  147: {2,4,4}

MATHEMATICA

Select[Range[100], #>1&&!PrimeQ[#]&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]

CROSSREFS

Cf. A000837, A007916, A018783, A056239, A108572, A112798, A289509, A318978, A327407, A327658.

Sequence in context: A274720 A338318 A322336 * A154384 A327756 A210251

Adjacent sequences:  A327682 A327683 A327684 * A327686 A327687 A327688

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 22 2019

STATUS

approved

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Last modified November 26 00:50 EST 2020. Contains 338631 sequences. (Running on oeis4.)