

A342669


Even numbers which are either primitively nondeficient (A006039), or become such after applying prime shift A003961 some number of times to them.


1



6, 20, 28, 70, 88, 104, 120, 180, 272, 300, 304, 368, 420, 464, 496, 504, 550, 572, 630, 650, 660, 748, 780, 836, 924, 990, 1020, 1050, 1092, 1140, 1170, 1184, 1312, 1376, 1380, 1430, 1470, 1504, 1650, 1696, 1740, 1860, 1870, 1888, 1952, 2002, 2090, 2210, 2220, 2310, 2460, 2470, 2530, 2580, 2584, 2730, 2820, 2856, 2990
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OFFSET

1,1


COMMENTS

Even numbers k for which A341624(k) = 1.
Even numbers whose closure under map x > A003961(x) contains a primitive nondeficient number (one of the terms of A006039). Shifting each term k exactly A336835(k)1 times with A003961 towards larger primes gives those numbers, but not in monotonic order, producing instead a permutation of A006039.
Sequence 2*A246277(A006039(.)), sorted into ascending order.
If there are any two terms, x and y, such that the other is a multiple of the other, then A336835(x) != A336835(y), and furthermore, for any term k present here, for all its proper divisors (dk, d<k) it holds that A336835(d) < A336835(k), in other words, they reach the deficiency earlier (by prime shifting) than k itself.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n)
Index entries for sequences computed from indices in prime factorization


EXAMPLE

For n = 120 = 2^3 * 3 * 5, A341620(120) = 8, so it is not primitive nondeficient. However, primeshifting it once gives A003961(120) = 945 = 3^3 * 5 * 7, which is one of the terms of A006039 as A341620(945) = 1. Therefore 120 is included in the sequence.


PROG

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A341620(n) = sumdiv(n, d, (sigma(d)>=(2*d)));
A341624(n) = { my(t, u=0); while((t=A341620(n))>0, u=t; n = A003961(n)); (u); };
isA342669(n) = (!(n%2)&&(1==A341624(n)));


CROSSREFS

Cf. A000396, A006039 (even terms of these form a subsequence).
Cf. A003961, A246277, A336835, A341605/A341606, A341620, A341624.
Sequence in context: A324649 A324643 A119425 * A006039 A180332 A338133
Adjacent sequences: A342666 A342667 A342668 * A342670 A342671 A342672


KEYWORD

nonn


AUTHOR

Antti Karttunen, Mar 20 2021


STATUS

approved



