A335331 -id:A335331 - cp's OEIS frontend

A128302 The indices of cubes (of primes) in the 3-almost primes.

1, 5, 30, 82, 328, 551, 1243, 1763, 3112, 6276, 7619, 12972, 17615, 20322, 26514, 37977, 52220, 57703, 76200, 90701, 98470, 124541, 144229, 177395, 229275, 258410, 273908, 306750, 324149, 360724, 510225, 559384, 638657, 666743, 819645, 852588

Offset: 1

Rick L. Shepherd, Feb 25 2007

nonn

the primepi function might be used to find terms. But it is expensive for larger numbers so then one might use A335331 to ease finding primepi(m) for larger m. - David A. Corneth, Apr 13 2025

			a(4) = 82 as 343 = 7^3 = prime(4)^3, the fourth cube in the 3-almost primes, is the eighty-second 3-almost prime.

Amiram Eldar, Table of n, a(n) for n = 1..590
David A. Corneth, PARI program

Cf. A000040, A014612, A030078, A128301, A128303, A335331.

Position[Select[Range[10^6], PrimeOmega[#] == 3 &], ?(PrimeNu[#] == 1 &)] // Flatten (* _Amiram Eldar, Apr 13 2025 *)

list(lim) = {my(f, c); for(k = 1, lim, f = factor(k); if(bigomega(f) == 3, c++; if(omega(f) == 1, print1(c, ", "))));} \\ Amiram Eldar, Apr 13 2025

PARI
```
\\ See Corneth link
```

A014612(a(n)) = A030078(n) = A000040(n)^3.

A341634 Smallest prime whose product of digits (A007954) is the n-th 7-smooth number = A002473(n), with a(0) = 101.

Original entry on oeis.org

101, 11, 2, 3, 41, 5, 23, 7, 181, 19, 251, 43, 127, 53, 281, 29, 541, 37, 83, 11551, 139, 47, 523, 1481, 157, 149, 12451, 67, 59, 283, 11177, 2551, 239, 1187, 1453, 79, 881, 257, 89, 1553, 2851, 199, 347, 563, 1483, 277, 14551, 1753, 269, 827, 853, 15551, 367

Offset: 0

Bernard Schott, Feb 16 2021

For n>=1, equals A107698 without the zeros.

101 is the smallest prime with the digit 0, so A007954(101) = 0 but as 0 is not a 7-smooth number, it is chosen a(0) = 101.

			83 is prime, A007954(83) = 8*3 = 24 that is the 18th 7-smooth number, and as no prime < 83 has a product of digits = 24, a(18) = 83.

David A. Corneth, Table of n, a(n) for n = 0..10000 (first 646 terms from Robert Israel)

Cf. A002473, A004954, A007954, A053666, A107698, A335331.

pod[n_] := Times @@ IntegerDigits[n]; seq[max_] := Module[{sm7 = Join[{0}, Select[Range[max], Max[FactorInteger[#][[;; , 1]]] <= 7 &]], m, s, n, c, i, ind}, m = Length[sm7]; s = Table[0, {m}]; n = 1; c = 0; While[c < m, n = NextPrime[n]; i = pod[n]; If[MemberQ[sm7, i], ind = Position[sm7, i][[1, 1]]]; If[s[[ind]] == 0, c++; s[[ind]] = n]]; s]; seq[150] (* Amiram Eldar, Feb 16 2021 *)

a(n) = A107698(A002473(n)) for n>=1. - Amiram Eldar, Feb 17 2021

More terms from Amiram Eldar, Feb 16 2021

cp's OEIS Frontend

A128302 The indices of cubes (of primes) in the 3-almost primes.

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