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A336314
a(n) = A324121(A122111(n)).
2
1, 1, 1, 2, 1, 12, 1, 2, 1, 4, 3, 2, 1, 12, 3, 2, 1, 12, 1, 6, 1, 4, 1, 8, 4, 36, 1, 10, 1, 24, 3, 2, 3, 4, 24, 4, 1, 12, 1, 56, 1, 24, 1, 2, 3, 4, 1, 4, 1, 6, 9, 6, 1, 4, 8, 8, 1, 12, 9, 48, 1, 4, 1, 2, 24, 120, 5, 2, 3, 18, 7, 12, 1, 36, 2, 10, 3, 24, 1, 12, 3, 4, 3, 112
OFFSET
1,4
FORMULA
a(n) = A324121(A122111(n)) = gcd(A323173(n), A122111(n)*A336315(n)).
PROG
(PARI)
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A324121(n) = gcd(sigma(n), n*numdiv(n));
(PARI)
\\ Or as a standalone program:
A336314(n) = if(1==n, 1, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, d=1, s=1, x=1, p, e); for(i=1, #es, pri += es[i]; p = prime(pri); e = 1+is[i]-is[1+i]; d *= e; s *= ((p^e)-1)/(p-1); x *= (p^(e-1))); gcd(s, x*d));
CROSSREFS
Cf. A336317 (gives the positions where this coincides with A323173).
Cf. also A335914.
Sequence in context: A074956 A176088 A069566 * A066818 A005730 A112284
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 19 2020
STATUS
approved