A392602 Numbers k such that A322582(k) <= A276086(k) <= A348507(k).

6, 8, 36, 64, 224, 243, 270, 432, 450, 630, 2325, 2349, 2372, 2376, 2400, 2532, 2552, 2556, 2560, 2736, 2760, 4625, 4652, 4656, 4680, 4832, 4836, 4860, 4864, 5040, 6932, 6936, 6960, 9240, 30056, 30075, 30076, 30080, 30100, 30102, 30104, 30126, 30128, 30132, 30150, 30256, 30264, 30280, 30282, 30288, 30304, 30330

Offset

1,1

Comments

A322582 and A348507 give lower and upper bound for arithmetic derivative, A003415. See comments in A351228.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10668

Index entries for sequences related to primorial base.

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A322582(n) = (n-A003958(n));
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348507(n) = (A003959(n) - n);
is_A392602(n) = { my(x=A276086(n)); ((x>=A322582(n)) && (x<=A348507(n))); };
(PARI) is_A392602(n) = if(!n, 0, my(f=factor(n), u=A348507(n), m=1, p=2, orgn=n); while(n, m *= (p^(n%p)); if(m>u, return(0)); n \= p; p = nextprime(1+p)); (m>=A322582(orgn))); \\ Antti Karttunen, Feb 10 2026

Crossrefs

Cf. A003415, A276086, A322582, A348507, A351228, A370127, A370128.

Subsequence of A393040, and thus of A393070. Apparently also a subsequence of A328118.

Cf. also A392601.

Sequence in context: A166642 A077709 A025627 * A038262 A054102 A261063

Adjacent sequences: A392599 A392600 A392601 * A392603 A392604 A392605

Keyword

nonn,base

Author

Antti Karttunen, Jan 21 2026

Status

approved