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For low median instead of mean we have A363941, triangle A124944A124943.

For high median instead of mean we have A363942, triangle A124943A124944.

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Cf. A102627, A215366, A327473, A327476, A327482, A348551, A359889, A363727, A363951.

Positions of integer mean are A316413, counted by A067538.

Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.

Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.

A088529/A088530 gives mean of prime signature A124010.

A067538 counts A316413 ranks partitions with integer mean, strict A102627counted by A067538.

`A088529/A088530 gives mean of prime signature A124010.

`A363947 ranks partitions with rounded mean 1, counted by A363948.

`A363950 ranks partitions with high mean 2, counted by A026905 redoubled.

Cf. A102627, A215366, A327473, A327476, A327482, A348551, `A359889, `A363723, `A363724, A363727, `A363731, A363951.

Extending the terminology introduced at A124943, this is the "low mean" of prime indices.

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

The case Positions of integer mean is are A316413, counted by A067538.

For low median instead of mean we have A363941, high A363942triangle A124944.

The For high version is A363944median instead of mean we have A363942, triangle A124943.

The high version is A363944, triangle for this statistic (low mean) is A363945, high A363946.

The triangle for this statistic (low mean) is A363945.

A008284 A067538 counts partitions by length, A058398 by with integer mean, strict A102627.

A051293 counts subsets with integer `A088529/A088530 gives mean, median A000975 of prime signature A124010.

A067538 counts partitions with integer mean, strict A102627, ranked by A316413 (complement A348551).

A088529/A088530 gives mean of prime signature A124010.

A316413 ranks partitions with integer mean, counted by A067538.

A360015 `A363947 ranks partitions with low mode rounded mean 1, counted by A241131A363948.

A363947 `A363950 ranks partitions with rounded high mean 1, 2, counted by A363948A026905 redoubled.

A363950 ranks partitions with high mean 2, counted by A026905 redoubled.

Cf. A215366 h_tri, A327473 h_mean_is_part, A327476 h_ptns_wo_mean, A327482, A359889 prix_mean_eq_medn, A363723 ptns_mean_is_unq_mode, A363724 ptns_mean_is_mode, A363727 prix_mean_eq_medn_eq_mode, A363731 ptns_mean_not_only_mode, A363951 prix_len_eq_mean.

Cf. A215366, A327473, A327476, A327482, A348551, `A359889, `A363723, `A363724, A363727, `A363731, A363951.

Mean of the multiset of prime indices of n, rounded down. Low mean of prime indices.

allocated for Gus WisemanMean of the multiset of prime indices of n, rounded down. Low mean of prime indices.

0, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 1, 6, 2, 2, 1, 7, 1, 8, 1, 3, 3, 9, 1, 3, 3, 2, 2, 10, 2, 11, 1, 3, 4, 3, 1, 12, 4, 4, 1, 13, 2, 14, 2, 2, 5, 15, 1, 4, 2, 4, 2, 16, 1, 4, 1, 5, 5, 17, 1, 18, 6, 2, 1, 4, 2, 19, 3, 5, 2, 20, 1, 21, 6, 2, 3, 4, 3, 22, 1, 2, 7

1,3

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 prime indices of 360 are {1,1,1,2,2,3}, with mean 3/2, so a(360) = 1.

meandown[y_]:=If[Length[y]==0, 0, Floor[Mean[y]]];

Table[meandown[prix[n]], {n, 100}]

Positions of first appearances are 1 and A000040.

The case of integer mean is A316413, counted by A067538.

Before rounding down we had A326567/A326568.

Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.

For mode instead of mean we have A363486, high A363487.

For median instead of mean we have A363941, high A363942.

The high version is A363944.

The triangle for this statistic (low mean) is A363945, high A363946.

A112798 lists prime indices, length A001222, sum A056239.

A008284 counts partitions by length, A058398 by mean.

A051293 counts subsets with integer mean, median A000975.

A067538 counts partitions with integer mean, strict A102627, ranked by A316413 (complement A348551).

A088529/A088530 gives mean of prime signature A124010.

A316413 ranks partitions with integer mean, counted by A067538.

A360005 gives twice the median of prime indices.

A360015 ranks partitions with low mode 1, counted by A241131.

A363947 ranks partitions with rounded mean 1, counted by A363948.

A363950 ranks partitions with high mean 2, counted by A026905 redoubled.

Cf. A215366 h_tri, A327473 h_mean_is_part, A327476 h_ptns_wo_mean, A327482, A359889 prix_mean_eq_medn, A363723 ptns_mean_is_unq_mode, A363724 ptns_mean_is_mode, A363727 prix_mean_eq_medn_eq_mode, A363731 ptns_mean_not_only_mode, A363951 prix_len_eq_mean.

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Gus Wiseman, Jun 29 2023

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