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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A112375, A064438.

A008474 is another version, defined for all n.

Sequence in context: A349215 A111611 A100478 * A161359 A363527 A224212

Adjacent sequences: A112373 A112374 A112375 * A112377 A112378 A112379

Keyword

nonn

Author

Zak Seidov, Dec 04 2005

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2006

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

Status

approved