A353813 a(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = [A004018(n) == 8], where [ ] is the Iverson bracket.

a(n) <= A353812(n), a(n) <= A353814(n).

Prog

(PARI) A353813(n) = { my(f = factor(n), nb1 = 0, p, ep); for(i=1, #f~, p = f[i, 1]; ep = f[i, 2]; if(1==(p%4), nb1++; if((ep>1)||(nb1>1), return(0))); if((3==(p%4)) && (ep%2), return(0))); return(1==nb1); }; \\ After "isok" function in A230779
(PARI)
A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018
A353813(n) = (8==A004018(n));

Crossrefs

Characteristic function of A230779.

Cf. A004018, A353814.

Differs from A353812 for the first time at n=325, where a(325) = 0, while A353812(325) = 1.

Sequence in context: A144601 A188009 A353812 * A353814 A144596 A188187

Adjacent sequences: A353810 A353811 A353812 * A353814 A353815 A353816

Keyword

nonn

Author

Antti Karttunen, May 14 2022

Status

approved