A095402 -id:A095402 - cp's OEIS frontend

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

Jonathan Vos Post, May 07 2006

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.

			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.

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

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

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).

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

A176717 Numbers n such that sum of digits of all distinct prime factors of n-th semiprime = sum of digits of all distinct prime factors of (n+1)-th semiprime.

Original entry on oeis.org

13, 15, 16, 20, 79, 91, 111, 116, 117, 119, 125, 131, 205, 215, 225, 250, 276, 282, 284, 298, 303, 313, 332, 340, 362, 364, 446, 501, 523, 554, 562, 686, 720, 728, 759, 796, 798, 830, 877, 904, 923, 925, 953, 962, 978, 986, 988, 992, 1007, 1056, 1097, 1117

Offset: 1

Juri-Stepan Gerasimov, Apr 24 2010

			a(1)=2 because 1st semiprime = 2*2 and 2=2; a(2)=5 because 2nd semiprime=2*3 and 2<3.

Cf. A095402, A176707.

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc: A176707 := proc(n) local p; p := numtheory[factorset](A001358(n)) ; add( A007953(d),d=p) ; end proc: isA176717 := proc(n) A176707(n) = A176707(n+1) ; end proc: for n from 1 to 1200 do if isA176717(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Apr 26 2010

Corrected (13 inserted, 20 inserted, 34 and 55 removed) and extended beyond 91 by R. J. Mathar, Apr 26 2010

cp's OEIS Frontend

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

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