A112376 Sum of base and exponent of prime powers.

3, 4, 4, 6, 8, 5, 5, 12, 14, 6, 18, 20, 24, 7, 6, 30, 32, 7, 38, 42, 44, 48, 9, 54, 60, 62, 8, 68, 72, 74, 80, 7, 84, 90, 98, 102, 104, 108, 110, 114, 13, 8, 128, 9, 132, 138, 140, 150, 152, 158, 164, 168, 15, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242

Offset: 1

Author

Zak Seidov, Dec 04 2005

Keywords

• nonn

Comments

If n = p^q, where p is prime and q > 0, then p+q is in the sequence.

If n is not of that form, omit the term.

Might be a good "puzzle" sequence - guess the rule given the first ten or so terms.

Examples

			n = 3 = 3^1, so 3+1 = 4 is a term; n = 4 = 2^2, so 2+2 = 4 is again a term; n = 5 = 5^1, so we get 5+1 =6.
But 6 is not a prime power, so we skip it.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A112375, A064438.

A008474 is another version, defined for all n.

Programs

Mathematica

fsum[a_] := Total[Flatten[FactorInteger[a]]]; fsum/@Select[Range[242], PrimePowerQ](* James C. McMahon, Jun 08 2024 *)

PARI

for(n=1,300,fac=factor(n);if(matsize(fac)[1]==1,print1(fac[1,1]+fac[1,2],",")))

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2006

Further edited by N. J. A. Sloane, Nov 19 2018