A075493 -id:A075493 - cp's OEIS frontend

A075492 Sum of digits of n < number of divisors of n.

10, 12, 20, 21, 24, 30, 32, 40, 42, 50, 60, 70, 72, 80, 90, 100, 102, 104, 105, 108, 110, 111, 112, 114, 120, 126, 130, 132, 140, 144, 150, 160, 162, 168, 180, 192, 200, 201, 204, 210, 212, 216, 220, 222, 224, 230, 231, 232, 234, 240, 250, 252, 260, 264, 270

Offset: 1

Labos Elemer, Sep 26 2002

			All are special composites.

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

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]-DivisorSigma[0, n]; If[s>0, Print[n]], {n, 1, 256}]
Select[Range[300],Total[IntegerDigits[#]]Harvey P. Dale, Apr 05 2015 *)

Solutions to A007953[x] < A000005[x]

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

Original entry on oeis.org

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

Labos Elemer, Sep 26 2002

			a[n]<0, see A075492, n=10, 20, 30, ... a[n]=0, see A057531, primes like 2, 11, 101 a[n]>0, see A075493, majority of primes and others

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

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

a(n)=A007953[n]-A000005[n]

A075494 Squares whose sum of digits exceeds the number of divisors.

Original entry on oeis.org

4, 9, 16, 25, 49, 64, 81, 121, 169, 196, 256, 289, 361, 484, 529, 625, 676, 729, 784, 841, 961, 1089, 1156, 1225, 1369, 1444, 1681, 1849, 1936, 2116, 2209, 2401, 2809, 3025, 3249, 3364, 3481, 3721, 3844, 3969, 4096, 4225, 4489, 4624, 4761, 5041, 5329

Offset: 1

Labos Elemer, Sep 26 2002

			Sequence consists mainly of squares of primes and of special composites like 33, 34, 35, 38, 44, 46.

Cf. A007953, A000005, A057531, A075491-A075493.

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]-DivisorSigma[0, n]; If[Greater[s, 0]&&IntegerQ[Sqrt[n]], Print[n]], {n, 1, 10000}]
Select[Range[80]^2,Total[IntegerDigits[#]]>DivisorSigma[0,#]&] (* Harvey P. Dale, Feb 16 2020 *)

Numbers k^2 such that A007953(k^2) > A000005(k^2).

Edited by Jon E. Schoenfield, Sep 23 2018

cp's OEIS Frontend

A075492 Sum of digits of n < number of divisors of n.

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

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Keywords

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Mathematica

Formula

A075494 Squares whose sum of digits exceeds the number of divisors.

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