A379681 Sum plus product of the multiset of prime indices of n.

1, 2, 4, 3, 6, 5, 8, 4, 8, 7, 10, 6, 12, 9, 11, 5, 14, 9, 16, 8, 14, 11, 18, 7, 15, 13, 14, 10, 20, 12, 22, 6, 17, 15, 19, 10, 24, 17, 20, 9, 26, 15, 28, 12, 19, 19, 30, 8, 24, 16, 23, 14, 32, 15, 23, 11, 26, 21, 34, 13, 36, 23, 24, 7, 27, 18, 38, 16, 29, 20

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.

Includes all positive integers.

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = A056239(n) + A003963(n).

The last position of k is 2^(k-1).

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Plus@@prix[n]+Times@@prix[n], {n, 30}]

Crossrefs

For prime factors instead of indices we have A075254, subtracted A075255.

Positions of first appearances are A379682.

For minus instead of plus we have A325036, which takes the following values:

- zero: A301987, counted by A001055

- negative: A325037, counted by A114324

- positive: A325038, counted by A096276 shifted right

- negative one: A325041, counted by A028422

- one: A325042, counted by A001055 shifted right

- nonnegative: A325044, counted by A096276

- nonpositive: A379721, counted by A319005

A000040 lists the primes, differences A001223.

A055396 gives least prime index, greatest A061395.

A056239 adds up prime indices, row sums of A112798, counted by A001222.

Cf. A000720, A003963, A178503, A175508, A319000, A325032, A325033, A325034, A325035, A325040.

Sequence in context: A330340 A328696 A053629 * A227370 A135761 A086305

Adjacent sequences: A379678 A379679 A379680 * A379682 A379683 A379684

Keyword

nonn,new

Author

Gus Wiseman, Jan 05 2025

Status

approved