A075491 Sum of digits of n minus number of divisors of n.

0, 0, 1, 1, 3, 2, 5, 4, 6, -3, 0, -3, 2, 1, 2, 2, 6, 3, 8, -4, -1, 0, 3, -2, 4, 4, 5, 4, 9, -5, 2, -1, 2, 3, 4, 0, 8, 7, 8, -4, 3, -2, 5, 2, 3, 6, 9, 2, 10, -1, 2, 1, 6, 1, 6, 3, 8, 9, 12, -6, 5, 4, 3, 3, 7, 4, 11, 8, 11, -1, 6, -3, 8, 7, 6, 7, 10, 7, 14, -2, 4, 6, 9, 0, 9, 10, 11, 8, 15, -3, 6, 5, 8, 9, 10, 3, 14, 11, 12, -8, 0, -5, 2, -3, -2, 3, 6, -3, 8, -6

Offset

1,5

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007953(n) - A000005(n).

Example

a(n) < 0 for n = 10, 20, 30, ... (A075492).
a(n) = 0 for n in A057531 which includes primes like 2, 11, 101.
a(n) > 0 for n in A075493 which includes the majority of primes and others.

Mathematica

sud[x_] := Apply[Plus, IntegerDigits[x]]; Table[sud[w]-DivisorSigma[0, w], {w, 1, 128}]
a[n_] := Total[IntegerDigits[n]]-DivisorSigma[0, n]; Array[a, 130] (* Harvey P. Dale, Aug 10 2011 *)

Prog

(PARI) a(n) = sumdigits(n) - numdiv(n); \\ Amiram Eldar, Mar 09 2026

Crossrefs

Cf. A000005, A007953, A057531, A075492, A075493.

Sequence in context: A053087 A316519 A062327 * A326730 A089279 A049820

Adjacent sequences: A075488 A075489 A075490 * A075492 A075493 A075494

Keyword

base,easy,sign

Author

Labos Elemer, Sep 26 2002

Status

approved