A118585 Sum of squares of digits of prime factors of n, with multiplicity.

0, 4, 9, 8, 25, 13, 49, 12, 18, 29, 2, 17, 10, 53, 34, 16, 50, 22, 82, 33, 58, 6, 13, 21, 50, 14, 27, 57, 85, 38, 10, 20, 11, 54, 74, 26, 58, 86, 19, 37, 17, 62, 25, 10, 43, 17, 65, 25, 98, 54, 59, 18, 34, 31, 27, 61, 91, 89, 106, 42

Offset: 1

Author

Jonathan Vos Post, May 07 2006

Keywords

• base
• easy
• nonn

Comments

Differs from A067666 if any prime factor exceeds 1 digit. Fixed points include 16, 27. See also: A067666 Sum of squares of prime factors of n (counted with multiplicity). See also: A003132 Sum of squares of digits of n. See also: A118503 Sum of digits of prime factors of n, with multiplicity.

Examples

			a(22) = 6 because 22 = 2 * 11 and the sum of squares of digits of prime factors is 2^2 + 1^2 + 1^2.
a(121) = 4 because 121 = 11^2 = 11 * 11, so 1^2 + 1^2 + 1^2 + 1^2 = 4.
		

Crossrefs

Cf. A001221, A001222, A003132, A005063, A007953, A007954, A067666, A095402, A118503.

Programs

Mathematica

Join[{0},Table[Total[Flatten[IntegerDigits/@(Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ n]])]^2],{n,2,60}]] (* Harvey P. Dale, Nov 17 2022 *)

Formula

a(n) = SUM[i=1..k] (e_i)*A003132(p_i) where prime decomposition of n = (p_1)^(e_1) * (p_2)^(e_2) * ... * (p_k)^(e_k).

Extensions

a(0) removed by Andrey Zabolotskiy, Jun 08 2024