A380345 a(n) = n + sum of prime indices of n.

1, 3, 5, 6, 8, 9, 11, 11, 13, 14, 16, 16, 19, 19, 20, 20, 24, 23, 27, 25, 27, 28, 32, 29, 31, 33, 33, 34, 39, 36, 42, 37, 40, 42, 42, 42, 49, 47, 47, 46, 54, 49, 57, 51, 52, 56, 62, 54, 57, 57, 60, 60, 69, 61, 63, 63, 67, 69, 76, 67, 79, 74, 71, 70, 74, 74, 86

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, with sum A056239.

Links

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

Formula

a(n) = n + A056239(n).

Example

72 has prime indices {1,1,1,2,2}, so a(72) = 72 + 7 = 79.

Mathematica

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

Crossrefs

For factors instead of indices we have A075254.

For minus instead of plus we have A178503.

Triangles:

- A027746 = prime factors

- A112798 = prime indices

Statistics:

- A000027 = product of prime factors = row products of A027746

- A001414 = sum of prime factors = row sums of A027746

- A003963 = product of prime indices = row products of A112798

- A056239 = sum of prime indices = row sums of A112798

Combinations:

- A075254 = product of factors + sum of factors = A000027 + A001414

- A075255 = product of factors - sum of factors = A000027 - A001414

- A178503 = product of factors - sum of indices = A000027 - A056239

- A325036 = product of indices - sum of indices = A003963 - A056239

- A379681 = product of indices + sum of indices = A003963 + A056239

- A380344 = product of indices - sum of factors = A003963 - A001414

- A380345 = product of factors + sum of indices = A000027 + A056239

- A380409 = product of indices + sum of factors = A003963 + A001414

A000040 lists the primes, differences A001223.

A001222 counts prime factors with multiplicity.

A055396 gives least prime index, greatest A061395.

Cf. A000720, A175508, A319000, A325032, A325033, A325034, A325035, A325040, A331384, A379682, A380220.

Sequence in context: A153264 A249595 A133561 * A095117 A184675 A336410

Adjacent sequences: A380342 A380343 A380344 * A380346 A380347 A380348

Keyword

nonn

Author

Gus Wiseman, Jan 25 2025

Status

approved