A074036 Sum of the primes from the smallest prime factor of n to the largest prime factor of n.

0, 2, 3, 2, 5, 5, 7, 2, 3, 10, 11, 5, 13, 17, 8, 2, 17, 5, 19, 10, 15, 28, 23, 5, 5, 41, 3, 17, 29, 10, 31, 2, 26, 58, 12, 5, 37, 77, 39, 10, 41, 17, 43, 28, 8, 100, 47, 5, 7, 10, 56, 41, 53, 5, 23, 17, 75, 129, 59, 10, 61, 160, 15, 2, 36, 28, 67, 58, 98, 17, 71, 5, 73, 197, 8

Offset

1,2

Comments

Obviously if n is prime then a(n) = n. However, there are composite values of n such that a(n) = n, such as 10 and 155. - Alonso del Arte, May 30 2017

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Erich Friedman, What's Special About This Number? Entry for 155.

Formula

Given p prime and k > 0, a(p^k) = p. - Alonso del Arte, May 30 2017

Example

a(14) = 17 because 14 = 2 * 7 and 2 + 3 + 5 + 7 = 17.

Maple

f:=proc(n) local i, t1, t2, t3, t4, t5, t6; if n<=1 then RETURN(0) else
t1:=ifactors(n); t2:=t1[2]; t3:=nops(t2); t4:=0; t5:=pi(t2[1][1]); t6:=pi(t2[t3][1]);
for i from t5 to t6 do t4:=t4+ithprime(i); od; RETURN(t4); fi; end; # N. J. A. Sloane, May 24 2010
# second Maple program:
s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end:
a:= proc(n) option remember; uses numtheory; `if`(n<2, 0, (m->
      s(pi(max(m)))-s(pi(min(m))-1))(factorset(n)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 24 2021

Mathematica

sp[n_]:=With[{fi=FactorInteger[n][[All, 1]]}, Total[Prime[Range[ PrimePi[ fi[[1]]], PrimePi[fi[[-1]]]]]]]; Join[{0}, Array[sp, 80, 2]] (* Harvey P. Dale, Dec 22 2017 *)

Prog

(PARI) a(n) = if (n==1, 0, my(f = factor(n), s = 0); forprime(p=f[1, 1], f[#f~, 1], s += p); s); \\ Michel Marcus, May 31 2017

Crossrefs

Cf. A055233, A169802, A169804.

Sequence in context: A008472 A318675 A123528 * A074251 A074196 A153023

Adjacent sequences: A074033 A074034 A074035 * A074037 A074038 A074039

Keyword

easy,nonn

Author

Jason Earls, Sep 15 2002

Status

approved