cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A358929 a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity).

Original entry on oeis.org

1, 19, 4, 316, 136, 760, 64, 4960, 22144, 103360, 27136, 5492224, 1186816, 41414656, 271212544, 559980544, 1334788096, 12943360, 7032930304, 527049293824, 158186536960, 1096295120896, 7871801589760, 154690378792960, 13071965224960, 56262393856, 964655941943296
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 06 2022

Keywords

Examples

			a(4) = 136, because 136 is a centered triangular number with 4 prime factors (counted with multiplicity) {2, 2, 2, 17} and this is the smallest such number.

Links

Crossrefs

Cf. A001222, A005448, A075088, A358926, A358927, A358928.

Programs

  • Mathematica
    c[k_] := (3*k^2 + 3*k + 2)/2; a[n_] := Module[{k = 0, ck}, While[PrimeOmega[ck = c[k]] != n, k++]; ck]; Array[a, 18, 0] (* Amiram Eldar, Dec 09 2022 *)
  • PARI
    a(n) = if(n==0, return(1)); for(k=1, oo, my(t=3*k*(k+1)/2 + 1); if(bigomega(t) == n, return(t))); \\ Daniel Suteu, Dec 10 2022

Extensions

a(22)-a(26) from Daniel Suteu, Dec 10 2022

A359234 a(n) is the smallest centered square number with exactly n distinct prime factors.

Original entry on oeis.org

1, 5, 85, 1105, 99905, 2339285, 294346585, 29215971265, 4274253515545, 135890190846085, 14289540733429585, 10285257499051999685, 659442750659021626765, 386961420250791449193065, 10019680253112694448155885, 7190322949201929673798425205, 944550762877225960238953138865
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 22 2022

Keywords

Examples

			a(4) = 99905, because 99905 is a centered square number with 4 distinct prime factors {5, 13, 29, 53} and this is the smallest such number.

Links

Crossrefs

Cf. A001221, A001844, A358894, A358928, A359235.

Programs

  • PARI
    a(n) = for(k=0, oo, my(t=2*k*k + 2*k + 1); if(omega(t) == n, return(t))); \\ Daniel Suteu, Dec 29 2022
  • PARI
    omega_centered_square_numbers(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(q%4==1, my(v=m*q, r=nextprime(q+1)); while(v <= B, if(j==1, if(v>=A, if (issquare((8*(v-1))/4 + 1) && ((sqrtint((8*(v-1))/4 + 1)-1)%2 == 0), listput(list, v))), if(v*r <= B, list=concat(list, f(v, r, j-1)))); v *= q))); list); vecsort(Vec(f(1, 2, n)));
a(n) = if(n==0, return(1)); my(x=vecprod(primes(n)), y=2*x); while(1, my(v=omega_centered_square_numbers(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Dec 29 2022

Extensions

a(8) from Jon E. Schoenfield, Dec 23 2022
a(9)-a(16) from Daniel Suteu, Dec 29 2022
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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