A379502 - OEIS

A379502

Characteristic function of almost Zumkeller numbers: a(n) = 1 if Zumkeller-deficiency of n (A103977) is 1, otherwise 0.

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

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OFFSET

LINKS

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

Index entries for characteristic functions.

FORMULA

a(n) = [A103977(n) = 1], where [ ] is the Iverson bracket.

a(n) = [A379504(n) > 0].

PROG

(PARI)

part(n, v) = if(n<1, return(n==0)); forstep(i=#v, 2, -1, if(part(n-v[i], v[1..i-1]), return(1))); n==v[1]

A379502(n) = my(d=concat(1, divisors(n)), s=sum(i=1, #d, d[i])); s%2==0 && part(s/2-n, d[1..#d-1]); \\ Amiram Eldar, Jan 06 2025, after Charles R Greathouse IV's Mar 09 2014 code in A083207.

CROSSREFS

Characteristic function of A379503.

Cf. A083207, A103977, A379504.

Sequence in context: A321083 A154269 A036987 * A354193 A354188 A342025

Adjacent sequences: A379499 A379500 A379501 * A379503 A379504 A379505

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 06 2025

STATUS

approved