A380760 Integers k with at least one proper factorization for which the sum of the same fixed integer power >= 2 of the factors equals k.
16, 27, 48, 54, 256, 270, 528, 1134, 1755, 2916, 3125, 7216, 7830, 11520, 11934, 15360, 19683, 22464, 30000, 31752, 40095, 40960, 46656, 65536, 69168, 81702, 86436, 93555, 100368, 146880, 200000, 212400, 264654, 273600, 291060, 303030, 317520, 340470, 362880
Offset: 1
Keywords
Examples
a(1) = 16: 2 * 2 * 2 * 2 = 2^2 + 2^2 + 2^2 + 2^2 = 16. a(5) = 256: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 = 256, and also 4 * 4 * 4 * 4 = 4^3 + 4^3 + 4^3 + 4^3 = 256. a(8) = 1134: 2 * 3 * 3 * 7 * 9 = 2^3 + 3^3 + 3^3 + 7^3 + 9^3 = 1134.
Programs
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PARI
a380760_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, my(c=0); for(p=2, oo, my(t=sum(i=1, #f, f[i]^p)); if(t
Extensions
Edited by Peter Munn, Mar 25 2025
Comments