A361867 - OEIS

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A361867

Positive integers > 1 whose prime indices satisfy (maximum) > 2*(median).

20, 28, 40, 44, 52, 56, 66, 68, 76, 78, 80, 84, 88, 92, 99, 102, 104, 112, 114, 116, 117, 120, 124, 132, 136, 138, 148, 152, 153, 156, 160, 164, 168, 170, 171, 172, 174, 176, 184, 186, 188, 190, 198, 200, 204, 207, 208, 212, 220, 222, 224, 228, 230, 232, 234

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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.

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

LINKS

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

EXAMPLE

The prime indices of 84 are {1,1,2,4}, with maximum 4 and median 3/2, and 4 > 2*(3/2), so 84 is in the sequence.

The terms together with their prime indices begin:

20: {1,1,3}

28: {1,1,4}

40: {1,1,1,3}

44: {1,1,5}

52: {1,1,6}

56: {1,1,1,4}

66: {1,2,5}

68: {1,1,7}

76: {1,1,8}

78: {1,2,6}

80: {1,1,1,1,3}

84: {1,1,2,4}

88: {1,1,1,5}

92: {1,1,9}

99: {2,2,5}

MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[100], Max@@prix[#]>2*Median[prix[#]]&]

CROSSREFS

The LHS is A061395 (greatest prime index).

The RHS is A360005 (twice median), distinct A360457.

The equal version is A361856, counted by A361849.

These partitions are counted by A361857, reverse A361858.

Including the equal case gives A361868, counted by A361859.

For mean instead of median we have A361907.

A000975 counts subsets with integer median.

A001222 counts prime factors, distinct A001221.

A112798 lists prime indices, sum A056239.

Cf. A053263, A067801, A111907, A237751, A237820, A359893, A361848, A361855, A361908, A361909.

Sequence in context: A368089 A367455 A350841 * A309769 A252478 A124318

Adjacent sequences: A361864 A361865 A361866 * A361868 A361869 A361870

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 05 2023

STATUS

approved