A390430 Least prime index of n plus greatest prime index of n; a(1) = 0.

0, 2, 4, 2, 6, 3, 8, 2, 4, 4, 10, 3, 12, 5, 5, 2, 14, 3, 16, 4, 6, 6, 18, 3, 6, 7, 4, 5, 20, 4, 22, 2, 7, 8, 7, 3, 24, 9, 8, 4, 26, 5, 28, 6, 5, 10, 30, 3, 8, 4, 9, 7, 32, 3, 8, 5, 10, 11, 34, 4, 36, 12, 6, 2, 9, 6, 38, 8, 11, 5, 40, 3, 42, 13, 5, 9, 9, 7, 44

Offset

1,2

Comments

First differs from A360457 at a(42) = 5, A360457(42) = 4. The prime indices of 42 are {1,2,4}, with median 2.

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..79.

Example

The prime indices of 42 are {1,2,4} so a(42) = 1 + 4 = 5.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, First[prix[n]]+Last[prix[n]]], {n, 1, 100}]

Crossrefs

For prime factors instead of indices we have A074320.

For difference instead of sum we have A243055, row sums of A355536.

For product instead of sum we have A333352.

Positions of odd terms are A390988, complement A391226.

Positions of first appearances appear to be A360006.

A055396 gives least prime index.

A061395 gives greatest prime index.

A112798 lists prime indices, sum A056239.

A390307 lists first sums of prime indices, see A390362, A390448, A390449, A390990.

A390363 adds up greatest two prime indices.

Cf. A124010, A243056, A286470, A355534, A390309.

Sequence in context: A354266 A360005 A360457 * A328985 A328196 A323307

Adjacent sequences: A390427 A390428 A390429 * A390431 A390432 A390433

Keyword

nonn

Author

Gus Wiseman, Nov 29 2025

Status

approved