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A324561 Numbers with at least one prime index equal to 0, 1, or 4 modulo 5. 2
2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 80, 82, 84, 86, 87 (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 counted by A039900. 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..66.

EXAMPLE

The sequence of terms together with their prime indices begins:

   2: {1}

   4: {1,1}

   6: {1,2}

   7: {4}

   8: {1,1,1}

  10: {1,3}

  11: {5}

  12: {1,1,2}

  13: {6}

  14: {1,4}

  16: {1,1,1,1}

  18: {1,2,2}

  20: {1,1,3}

  21: {2,4}

  22: {1,5}

  23: {9}

  24: {1,1,1,2}

MAPLE

with(numtheory):

q:= n-> is(irem(pi(min(factorset(n))), 5) in {0, 1, 4}):

select(q, [$2..100])[];  # Alois P. Heinz, Mar 07 2019

MATHEMATICA

Select[Range[100], Intersection[Mod[If[#==1, {}, PrimePi/@First/@FactorInteger[#]], 5], {0, 1, 4}]!={}&]

CROSSREFS

Cf. A008854, A039900, A055396, A056239, A061395, A106529, A112798.

Cf. A324519, A324521, A324522, A324560, A324561, A324562.

Sequence in context: A014530 A268445 A053663 * A288258 A075313 A183858

Adjacent sequences:  A324558 A324559 A324560 * A324562 A324563 A324564

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 06 2019

STATUS

approved

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Last modified September 27 17:05 EDT 2021. Contains 347693 sequences. (Running on oeis4.)