A390364 Numbers whose prime indices are the first sums minus 1 of some multiset beginning with 1. Sorted list of all Heinz numbers of rows of A390308. Union of A390309.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 78, 79, 80, 82

Offset

1,2

Comments

First differs from A325389 in having 75.

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..67.

Example

The prime indices of 25 are (3,3), which is not the first sums minus 1 of any multiset beginning with 1 (note (2,2,2) does not begin with 1), so 25 is not in the sequence.
The prime indices of 39 are (2,6), which is the first sums minus 1 of (1,2,5), so 39 is in the sequence.

Mathematica

nn=100;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
firsums[c_]:=Table[c[[i]]+c[[i+1]], {i, Length[c]-1}];
Take[Sort[Table[Times@@Prime/@(firsums[Prepend[prix[n], 1]]-1), {n, Prime[nn]}]], nn]

Crossrefs

This is the sorted version of A390309, triangle A390308.

The complement is A390365.

The non-prepended complement is A390445, counted by A390447.

The non-prepended version is A390448, counted by A390446.

The non-prepended non-sorted version is A390449.

A112798 lists prime indices, sum A056239.

A243056 gives maximum prime index minus minimum prime index.

A358169 gives first differences plus one of 1-prepended prime indices, reverse A355534.

A390307 lists first sums of prime indices, for differences A355536.

Cf. A000040, A001222, A055396, A093641, A174090, A243055, A325351, A325352, A355531.

Sequence in context: A122132 A347248 A347243 * A325389 A020662 A306202

Adjacent sequences: A390361 A390362 A390363 * A390365 A390366 A390367

Keyword

nonn

Author

Gus Wiseman, Nov 20 2025

Status

approved