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A320325 Numbers whose product of prime indices is a perfect power. 19
7, 9, 14, 18, 19, 21, 23, 25, 27, 28, 36, 38, 42, 46, 49, 50, 53, 54, 56, 57, 63, 72, 76, 81, 84, 92, 97, 98, 100, 103, 106, 108, 112, 114, 115, 121, 125, 126, 131, 133, 144, 147, 151, 152, 159, 161, 162, 168, 169, 171, 175, 183, 184, 185, 189, 194, 195, 196 (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.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

The terms together with their corresponding multiset multisystems (A302242):

   7: {{1,1}}

   9: {{1},{1}}

  14: {{},{1,1}}

  18: {{},{1},{1}}

  19: {{1,1,1}}

  21: {{1},{1,1}}

  23: {{2,2}}

  25: {{2},{2}}

  27: {{1},{1},{1}}

  28: {{},{},{1,1}}

  36: {{},{},{1},{1}}

  38: {{},{1,1,1}}

  42: {{},{1},{1,1}}

  46: {{},{2,2}}

  49: {{1,1},{1,1}}

  50: {{},{2},{2}}

  53: {{1,1,1,1}}

  54: {{},{1},{1},{1}}

  56: {{},{},{},{1,1}}

  57: {{1},{1,1,1}}

  63: {{1},{1},{1,1}}

  72: {{},{},{},{1},{1}}

  76: {{},{},{1,1,1}}

  81: {{1},{1},{1},{1}}

MATHEMATICA

Select[Range[100], GCD@@FactorInteger[Times@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]^k]][[All, 2]]>1&]

CROSSREFS

Cf. A000720, A001222, A001597, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A320322, A320323, A320324.

Sequence in context: A145827 A116025 A344011 * A320699 A332514 A305214

Adjacent sequences:  A320322 A320323 A320324 * A320326 A320327 A320328

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 10 2018

STATUS

approved

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Last modified November 27 19:06 EST 2021. Contains 349394 sequences. (Running on oeis4.)