A360130 - OEIS

A360130

a(n) = 1 if A003961(n) is a triangular number, otherwise 0, where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A010054(A003961(n)).

EXAMPLE

For n = 99 = 9*11, A003961(99) = 325 = 25*13, and 325 is one of the (odd) triangular numbers, A014493, therefore a(99) = 1.

MATHEMATICA

f[p_, e_] := NextPrime[p]^e; a[n_] := If[IntegerQ[Sqrt[8*Times @@ f @@@ FactorInteger[n] + 1]], 1, 0]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A010054(n) = issquare(8*n + 1);

A360130(n) = A010054(A003961(n));

CROSSREFS

Cf. A003961, A010054, A014493.

Sequence in context: A255849 A185059 A179776 * A353570 A089802 A089801

Adjacent sequences: A360127 A360128 A360129 * A360131 A360132 A360133

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 12 2023

STATUS

approved