A368728 - OEIS

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A368728

Numbers whose prime indices are 1, prime, or semiprime.

3

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 75

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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..67.

FORMULA

Closed under multiplication.

MATHEMATICA

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

Select[Range[100], Max@@Length/@prix/@prix[#]<=2&]

CROSSREFS

These are products of primes indexed by elements of A037143.

For just primes we have A076610, strict A302590.

For just semiprimes we have A339112, strict A340020.

For squarefree semiprimes we have A339113, strict A309356.

The odd case is A368729, strict A340019.

The complement is A368833.

A000607 counts partitions into primes, A034891 with ones allowed.

A001358 lists semiprimes, squarefree A006881.

A006450, A106349, A322551, A368732 list selected primes.

A056239 adds up prime indices, row sums of A112798.

A101048 counts partitions into semiprimes.

Cf. A000040, A000720, A001222, A003963, A005117, A302242, A320628, A320911, A320912.

Sequence in context: A242474 A351374 A160544 * A276568 A295020 A298359

Adjacent sequences: A368725 A368726 A368727 * A368729 A368730 A368731

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 07 2024

STATUS

approved