The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360356

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A360356

Primitive terms of A360332: terms of A360332 with no proper divisor in A360332.
(history; published version)

#9 by Joerg Arndt at Mon Feb 06 01:28:09 EST 2023

STATUS

proposed

approved

#8 by Amiram Eldar at Mon Feb 06 00:23:23 EST 2023

STATUS

editing

proposed

#7 by Amiram Eldar at Mon Feb 06 00:21:33 EST 2023

LINKS

Amiram Eldar, <a href="/A360356/b360356.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#6 by N. J. A. Sloane at Sat Feb 04 20:57:01 EST 2023

STATUS

proposed

approved

#5 by Amiram Eldar at Sat Feb 04 03:12:48 EST 2023

STATUS

editing

proposed

#4 by Amiram Eldar at Sat Feb 04 03:09:55 EST 2023

COMMENTS

Analogous to primitive abundant numbers (A091191) with divisors that are restricted to numbers that have only nonprime-indexed prime factors.

#3 by Amiram Eldar at Sat Feb 04 03:07:23 EST 2023

COMMENTS

If m is a term then then k*m is a term of A360332 for all k in A320628.

#2 by Amiram Eldar at Sat Feb 04 02:35:56 EST 2023

NAME

allocated for Amiram EldarPrimitive terms of A360332: terms of A360332 with no proper divisor in A360332.

DATA

56, 104, 196, 304, 364, 368, 464, 532, 644, 812, 1036, 1184, 1204, 1316, 1376, 1484, 1504, 1696, 1708, 1952, 1988, 2044, 2212, 2492, 2716, 2828, 2884, 2996, 3164, 3496, 3668, 3836, 3892, 4172, 4228, 4408, 4544, 4564, 4672, 4676, 4844, 5056, 5068, 5336, 5404, 5516

OFFSET

1,1

COMMENTS

If m is a term then then k*m is a term of A360332 for all k in A320628.

MATHEMATICA

f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, (p^(e + 1) - 1)/(p - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; primQ[n_] := s[n] > 2*n && AllTrue[Divisors[n], # == n || s[#] <= 2*# &]; Select[Range[6000], primQ]

PROG

(PARI) isab(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), 1, (p[i]^(e[i]+1)-1)/(p[i]-1))) > 2*n; }

is(n) = {if(!isab(n), return(0)); fordiv(n, d, if(d < n && isab(d), return(0))); return(1)};

CROSSREFS

Subsequence of A360332.

Cf. A320628.

Similar sequences: A006038, A091191, A249263, A302574, A360355.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Feb 04 2023

STATUS

approved

editing

#1 by Amiram Eldar at Sat Feb 04 02:26:07 EST 2023

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved