A366319 Numbers k such that the sum of prime indices of k is not twice the maximum prime index of k, meaning A056239(k) != 2 * A061395(k).

1, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76

Offset

1,2

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 integer partitions containing n/2, where n is the sum of all parts.

Links

Table of n, a(n) for n=1..67.

Example

The prime indices of 90 are {1,2,2,3}, with sum 8 and twice maximum 6, so 90 is in the sequence.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Max[prix[#]]!=Total[prix[#]]/2&]

Crossrefs

Partitions of this type are counted by A086543.

For length instead of maximum we have the complement of A340387.

The complement is A344415, counted by A035363.

A001221 counts distinct prime factors, A001222 with multiplicity.

A056239 adds up prime indices, row sums of A112798.

A334201 adds up all prime indices except the greatest.

A344291 lists numbers m with A001222(m) <= A056239(m)/2, counted by A110618.

A344296 lists numbers m with A001222(m) >= A056239(m)/2, counted by A025065.

Cf. A001414, A100959, A238628, A300061, A301987, A316413, A320924, A344414, A344416, A366318.

Sequence in context: A048964 A028749 A028764 * A326070 A337050 A304364

Adjacent sequences: A366316 A366317 A366318 * A366320 A366321 A366322

Keyword

nonn

Author

Gus Wiseman, Oct 10 2023

Status

approved