A379682 Least number whose prime indices have sum + product = n.

1, 2, 4, 3, 6, 5, 10, 7, 14, 11, 15, 13, 26, 17, 25, 19, 33, 23, 35, 29, 58, 31, 51, 37, 74, 41, 65, 43, 69, 47, 85, 53, 105, 59, 93, 61, 122, 67, 115, 71, 123, 73, 145, 79, 158, 83, 141, 89, 161, 97, 185, 101, 177, 103, 205, 107, 214, 109, 201, 113, 226, 127

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.

Links

Table of n, a(n) for n=1..62.

Example

The positions of 11 in A379681 are: 15, 22, 56, 72, 160, 384, 1024, so a(11) = 15.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
sp=Table[Plus@@prix[n]+Times@@prix[n], {n, 1000}];
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
Table[Position[sp, n][[1, 1]], {n, mnrm[sp]}]

Crossrefs

Position of first appearance of n in A379681.

The subtraction A325036 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, A075254, A178503, A175508, A319000, A325032, A325033, A325034, A325035, A325040.

Sequence in context: A375563 A384045 A091857 * A232642 A180625 A132340

Adjacent sequences: A379679 A379680 A379681 * A379683 A379684 A379685

Keyword

nonn

Author

Gus Wiseman, Jan 05 2025

Status

approved