A283983 Square root of the largest square dividing prime factorization representation of the n-th Stern polynomial: a(n) = A000188(A260443(n)).

1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 3, 1, 15, 1, 1, 1, 3, 5, 15, 7, 45, 5, 15, 1, 15, 35, 15, 1, 105, 1, 1, 1, 3, 5, 105, 7, 225, 35, 525, 11, 1575, 175, 1125, 7, 1575, 35, 105, 1, 105, 35, 525, 77, 1575, 35, 525, 1, 105, 385, 105, 1, 1155, 1, 1, 1, 3, 5, 1155, 7, 1575, 385, 3675, 11, 7875, 1225, 275625, 77, 55125, 2695, 5775, 13, 17325, 13475, 275625, 539

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..4096

Formula

a(n) = A000188(A260443(n)).

a(n) = A000196(A283989(n)).

Other identities. For all n >= 0:

a(2n) = A003961(a(n)).

A001222(a(n)) = A284264(n).

Mathematica

A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_] := A003961[n] = Times @@ ( A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n]  (* after Jean-François Alcover, Dec 01 2011 *); A260443[n_]:= If[n<2, n + 1, If[EvenQ[n], A003961[A260443[n/2]], A260443[(n - 1)/2] * A260443[(n + 1)/2]]];  A000188[n_]:= Sum[Boole[Mod[i^2, n] == 0], {i, n}]; Table[A000188[A260443[n]], {n, 0, 50}] (* Indranil Ghosh, Mar 28 2017 *)

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2)))); \\ Cf. Charles R Greathouse IV's code for "ps" in A186891 and A277013.
A000188(n) = core(n, 1)[2]; \\ This function from Michel Marcus, Feb 27 2013
A283983(n) = A000188(A260443(n));
(Scheme)
(define (A283983 n) (A000188 (A260443 n)))
(define (A283983 n) (A000196 (A283989 n)))

Crossrefs

Cf. A000188, A000196, A001222, A003961, A260443, A283989, A284264, A283484 (odd bisection).

Cf. A023758 (positions of ones).

Sequence in context: A131270 A109223 A263009 * A016466 A293669 A055210

Adjacent sequences: A283980 A283981 A283982 * A283984 A283985 A283986

Keyword

nonn

Author

Antti Karttunen, Mar 25 2017

Status

approved