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

1,2

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.

Links

Table of n, a(n) for n=1..60.

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).

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A065642 A285109 A217579 * A067666 A355012 A280286

Adjacent sequences: A118582 A118583 A118584 * A118586 A118587 A118588

Keyword

base,easy,nonn

Author

Jonathan Vos Post, May 07 2006

Extensions

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

Status

approved