OFFSET
0,2
REFERENCES
P. M. B. Vitanyi, Lindenmayer Systems: Structure, Languages and Growth Functions, Mathematisch Centrum, Math. Centre Tracts #96, 1980, p. 25.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
O. Osterby, Prime decompositions with minimum sum, Matematisk Institut, Aarhus Universitet, Technical Report DAIMI PB-19, November 1973; see the third column of Table 5 on page 18.
O. Osterby, Prime decompositions with minimum sum, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), 451-458.
FORMULA
Max { Prod p^a + d : Sum p^a + d = n }, p prime.
a(n) = max(a(n-1)+1, A051703(n)). - Andrew Howroyd, Jan 05 2018
EXAMPLE
a(11) = 31 because we can write 11 = 1 + 2 + 3 + 5 and 31 = 1+2*3*5.
PROG
(PARI) \\ here s is A051703 as a vector
s(n)={my(v=vector(n+1)); v[1]=1; forprime(p=2, n, forstep(i=#v, 1, -1, my(q=1); while(q*p<i, q*=p; v[i]=max(v[i], q*v[i-q])))); v}
seq(n)={my(v=s(n)); for(i=2, #v, v[i]=max(v[i], v[i-1]+1)); v} \\ Andrew Howroyd, Jan 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
First 4 values appear incorrectly in cited references; corrected by JOS
a(0)=1 and terms a(35) and beyond from Andrew Howroyd, Jan 05 2018
STATUS
approved